# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/38.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1150.png"
 ALT="$38.8'$">|; 

$key = q/Deltabar{F};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1221.png"
 ALT="$\Delta\bar{F}$">|; 

$key = q/119.064;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1493.png"
 ALT="$119.064$">|; 

$key = q/-3^circ27';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="$-3^\circ 27'$">|; 

$key = q/-23^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="$-23^\circ 26'$">|; 

$key = q/+38^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="$+38^\circ 26'$">|; 

$key = q/{displaymath}a_{{rm{+}=90^circ-|L-delta|.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="\begin{displaymath}
a_{\rm +} = 90^\circ - \vert L-\delta\vert.
\end{displaymath}">|; 

$key = q/W;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$W$">|; 

$key = q/88.057;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1777.png"
 ALT="$88.057$">|; 

$key = q/06.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1087.png"
 ALT="$06.8'$">|; 

$key = q/-278.996;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1274.png"
 ALT="$-278.996$">|; 

$key = q/92.8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="$92.8$">|; 

$key = q/{displaymath}mu=lambda_S-bar{lambda}-q=273.055-60.464-10.739=201.852simeq202^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1780.png"
 ALT="\begin{displaymath}
\mu=\lambda_S - \bar{\lambda}-q = 273.055-60.464-10.739= 201.852\simeq202^\circ.
\end{displaymath}">|; 

$key = q/{displaymath}tilde{D}=bar{lambda}-lambda_S=358.883-44.602=314.281^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1256.png"
 ALT="\begin{displaymath}
\tilde{D}=\bar{\lambda}-\lambda_S = 358.883-44.602 = 314.281^\circ.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere9.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="337" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere9.eps}}
\end{figure}">|; 

$key = q/bar{lambda}_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1463.png"
 ALT="$\bar{\lambda}_M$">|; 

$key = q/{displaymath}Theta_-(0.83)=0.071,mbox{hspace{0.5cm}}Theta_+(0.83)=0.759,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1858.png"
 ALT="\begin{displaymath}
\Theta_-(0.83) = 0.071, \mbox{\hspace{0.5cm}}\Theta_+(0.83) = 0.759,
\end{displaymath}">|; 

$key = q/156^d22^h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="$156^d22^h$">|; 

$key = q/18.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1124.png"
 ALT="$18.0'$">|; 

$key = q/CP^2=CQ^2+QP^2-2,CQ,QP,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="$CP^2 = CQ^2+QP^2-2 CQ QP \cos M$">|; 

$key = q/displaystyle(cosA,{{bf{e}-sinA,{{bf{n})times{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$\displaystyle (\cos A  {\bf e}-\sin A {\bf n})\times {\bf r}$">|; 

$key = q/43.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img995.png"
 ALT="$43.6'$">|; 

$key = q/b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2159.png"
 ALT="$b$">|; 

$key = q/60.464;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1776.png"
 ALT="$60.464$">|; 

$key = q/leftrightarrow;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\leftrightarrow$">|; 

$key = q/displaystylefrac{cosdelta,sint}{cosL,sindelta-sinL,cosdelta,cost},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$\displaystyle \frac{\cos \delta \sin t}{\cos L \sin \delta - \sin L \cos\delta \cos t},$">|; 

$key = q/{displaymath}Theta_-(0.90)=0.045,mbox{hspace{0.5cm}}Theta_+(0.90)=0.855,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1932.png"
 ALT="\begin{displaymath}
\Theta_-(0.90) = 0.045,\mbox{\hspace{0.5cm}}\Theta_+(0.90) = 0.855,
\end{displaymath}">|; 

$key = q/41.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img941.png"
 ALT="$41.8'$">|; 

$key = q/41.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img935.png"
 ALT="$41.6'$">|; 

$key = q/2453026.4+5times29.53simeq2453174.1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1477.png"
 ALT="$2453026.4
+ 5\times 29.53\simeq 2453174.1$">|; 

$key = q/52.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img972.png"
 ALT="$52.8'$">|; 

$key = q/{displaymath}cosbar{mu}simeq-frac{(bar{a}^2+n_Sslashn)}{bar{a},(1+n_Sslashn)}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1813.png"
 ALT="\begin{displaymath}
\cos\bar{\mu} \simeq - \frac{(\bar{a}^2 + n_S/n)}{\bar{a} (1+n_S/n)}.
\end{displaymath}">|; 

$key = q/mu=252.692^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2128.png"
 ALT="$\mu= 252.692^\circ$">|; 

$key = q/358.883;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1253.png"
 ALT="$358.883$">|; 

$key = q/305.796;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2059.png"
 ALT="$305.796$">|; 

$key = q/16.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1070.png"
 ALT="$16.2'$">|; 

$key = q/{Delta}t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="${\Delta} t$">|; 

$key = q/bar{F}=337.132^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1315.png"
 ALT="$\bar{F}=337.132^\circ$">|; 

$key = q/55.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1056.png"
 ALT="$55.6'$">|; 

$key = q/r_Ssimeqa_S,(1-e_S,cosM_S);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1549.png"
 ALT="$r_S\simeq a_S (1-e_S \cos M_S)$">|; 

$key = q/18.5%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1614.png"
 ALT="$18.5\%$">|; 

$key = q/+70^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$+70^\circ $">|; 

$key = q/+26^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="$+26^\circ 34'$">|; 

$key = q/WP=ZW+ZP=XL+ZP=2,e,a,sinM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="$WP = ZW+ZP = XL+ZP = 2 e a \sin M$">|; 

$key = q/RP=r,sinT;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="$RP=r \sin T$">|; 

$key = q/2^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1360.png"
 ALT="$2^\circ$">|; 

$key = q/1';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$1'$">|; 

$key = q/+0.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="$+0.9$">|; 

$key = q/{displaymath}z=(1-zeta_S)slash(1-zeta)=(1+8.56times10^{-3})slash(1-2.72times10^{-3})=1.01131.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1905.png"
 ALT="\begin{displaymath}
z= (1-\zeta_S)/(1-\zeta) = (1+8.56\times 10^{-3})/(1-2.72\times 10^{-3}) =
1.01131.
\end{displaymath}">|; 

$key = q/rho_S>rho_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1584.png"
 ALT="$\rho_S&gt;\rho_M$">|; 

$key = q/32.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img952.png"
 ALT="$32.2'$">|; 

$key = q/41.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img917.png"
 ALT="$41.0'$">|; 

$key = q/0.294^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1795.png"
 ALT="$0.294^\circ$">|; 

$key = q/Theta_+=-0.125;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2115.png"
 ALT="$\Theta_+ = -0.125$">|; 

$key = q/162.130;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1892.png"
 ALT="$162.130$">|; 

$key = q/23.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img987.png"
 ALT="$23.4'$">|; 

$key = q/{displaymath}F=bar{F}+q=266.549-16.974=249.575simeq250^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2136.png"
 ALT="\begin{displaymath}
F = \bar{F} + q = 266.549-16.974= 249.575\simeq 250^\circ.
\end{displaymath}">|; 

$key = q/204.436;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2133.png"
 ALT="$204.436$">|; 

$key = q/z=z_{{rm{max};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1682.png"
 ALT="$z=z_{\rm max}$">|; 

$key = q/XCPi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="$XC\Pi$">|; 

$key = q/43';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="$43'$">|; 

$key = q/-324.337;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1915.png"
 ALT="$-324.337$">|; 

$key = q/21.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img939.png"
 ALT="$21.8'$">|; 

$key = q/DeltaM_M(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1623.png"
 ALT="$\Delta M_M (^\circ)$">|; 

$key = q/displaystyle1-e,cosM+2,e^2,sin^2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="$\displaystyle 1 -e \cos M + 2 e^2 \sin^2 M,$">|; 

$key = q/deltatheta_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1725.png"
 ALT="$\delta\theta_+$">|; 

$key = q/383.163;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1848.png"
 ALT="$383.163$">|; 

$key = q/42.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img965.png"
 ALT="$42.6'$">|; 

$key = q/{displaymath}bar{F}=bar{F}_0+breve{n},(t-t_0).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2014.png"
 ALT="\begin{displaymath}
\bar{F} = \bar{F}_0 + \breve{n} (t-t_0).
\end{displaymath}">|; 

$key = q/350.223;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2119.png"
 ALT="$350.223$">|; 

$key = q/-3.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1376.png"
 ALT="$-3.00$">|; 

$key = q/bar{z}=1.00118;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1855.png"
 ALT="$\bar{z}= 1.00118$">|; 

$key = q/bar{mu};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1945.png"
 ALT="$\bar{\mu}$">|; 

$key = q/-335.375;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1523.png"
 ALT="$-335.375$">|; 

$key = q/XR;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$XR$">|; 

$key = q/1.60213807;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2148.png"
 ALT="$1.60213807$">|; 

$key = q/54.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1026.png"
 ALT="$54.6'$">|; 

$key = q/+6^circ06';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="$+6^\circ 06'$">|; 

$key = q/rho_{S,0}=R_Sslasha_S=6.960times10^5,{{rm{km}slash1.496times10^8,{{rm{km}simeq15.99';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1552.png"
 ALT="$\rho_{S 0}=R_S/a_S=6.960\times10^5 {\rm km}/1.496\times 10^8 {\rm km}\simeq 15.99'$">|; 

$key = q/A';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1650.png"
 ALT="$A'$">|; 

$key = q/360slash0.46157617=779.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1804.png"
 ALT="$360/0.46157617= 779.9$">|; 

$key = q/Deltabar{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1466.png"
 ALT="$\Delta \bar{D}$">|; 

$key = q/236.791;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1965.png"
 ALT="$236.791$">|; 

$key = q/{displaymath}beta_0(350^circ)=-0.423^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2121.png"
 ALT="\begin{displaymath}
\beta_0(350^\circ) = -0.423^\circ.
\end{displaymath}">|; 

$key = q/bar{F}_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2025.png"
 ALT="$\bar{F}_0$">|; 

$key = q/45.8^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1984.png"
 ALT="$45.8^\circ$">|; 

$key = q/115.416;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1847.png"
 ALT="$115.416$">|; 

$key = q/tau;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="$\tau$">|; 

$key = q/q=-0.091^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2069.png"
 ALT="$q= -0.091^\circ$">|; 

$key = q/n_M-n_S=13.17639646-0.98564735=12.1907491^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1475.png"
 ALT="$n_M - n_S = 13.17639646-0.98564735=12.1907491^\circ$">|; 

$key = q/+33^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="$+33^\circ 26'$">|; 

$key = q/a_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1328.png"
 ALT="$a_M$">|; 

$key = q/23.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img975.png"
 ALT="$23.0'$">|; 

$key = q/PSW;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="$PSW$">|; 

$key = q/Deltabar{F}(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1425.png"
 ALT="$\Delta \bar{F}(^\circ)$">|; 

$key = q/25.6^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1997.png"
 ALT="$25.6^\circ$">|; 

$key = q/displaystylecosL,cosalpha_0,{{bf{v}+(sinL,sinepsilon+cosL,cosepsilon,sinalpha_0),{{bf{s}+(sinL,cosepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$\displaystyle \cos L \cos \alpha_0 {\bf v} + (\sin L \sin\epsilon + \cos L \cos\epsilon \sin \alpha_0) {\bf s} + (\sin L \cos\epsilon$">|; 

$key = q/{displaymath}tilde{n}=n-varpi_1{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="\begin{displaymath}
\tilde{n} = n - \varpi_1
\end{displaymath}">|; 

$key = q/bar{F}_0=305.796^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1866.png"
 ALT="$\bar{F}_0 =305.796^\circ$">|; 

$key = q/2.046;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1961.png"
 ALT="$2.046$">|; 

$key = q/-314.412;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1770.png"
 ALT="$-314.412$">|; 

$key = q/109.717;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1492.png"
 ALT="$109.717$">|; 

$key = q/q_1=6.239^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1569.png"
 ALT="$q_1=6.239^\circ$">|; 

$key = q/03.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img985.png"
 ALT="$03.4'$">|; 

$key = q/25.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1035.png"
 ALT="$25.0'$">|; 

$key = q/67.003;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1900.png"
 ALT="$67.003$">|; 

$key = q/+10^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$+10^\circ $">|; 

$key = q/45.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1043.png"
 ALT="$45.2'$">|; 

$key = q/displaystyleE-e,sinE,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="$\displaystyle E - e \sin E,$">|; 

$key = q/beta_{M}(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1609.png"
 ALT="$\beta_{M}(')$">|; 

$key = q/displaystyle0.422,e_M,sin(2bar{D}-M_M),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1453.png"
 ALT="$\displaystyle 0.422 e_M \sin (2\bar{D} - M_M),$">|; 

$key = q/59.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1164.png"
 ALT="$59.2'$">|; 

$key = q/-5.51;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1362.png"
 ALT="$-5.51$">|; 

$key = q/displaystyleh;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2036.png"
 ALT="$\displaystyle h$">|; 

$key = q/PSL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$PSL$">|; 

$key = q/14^h21^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="$14^h21^m$">|; 

$key = q/15.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1058.png"
 ALT="$15.8'$">|; 

$key = q/{displaymath}z=(1-zeta_S)slash(1-zeta)=(1-1.662times10^{-2})slash(1+4.38times10^{-3})=0.97909,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1930.png"
 ALT="\begin{displaymath}
z= (1-\zeta_S)/(1-\zeta) = (1-1.662\times 10^{-2})/(1+4.38\times 10^{-3}) =
0.97909,
\end{displaymath}">|; 

$key = q/199^circ51'slash15^circ=13^h14^m.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$199^\circ 51'/15^\circ = 13^h 14^m.$">|; 

$key = q/dbar{lambda}slashdt=n;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1809.png"
 ALT="$d\bar{\lambda}/dt= n$">|; 

$key = q/q_2(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1431.png"
 ALT="$q_2(^\circ)$">|; 

$key = q/104.993;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1236.png"
 ALT="$104.993$">|; 

$key = q/{displaymath}tsimeqt_0+(360-284.998)slash0.46157617simeqt_0+162,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1791.png"
 ALT="\begin{displaymath}
t\simeq t_0 + (360-284.998)/0.46157617\simeq t_0 + 162  {\rm JD}.
\end{displaymath}">|; 

$key = q/displaystyle-0.038,e,sin2bar{F},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1208.png"
 ALT="$\displaystyle -0.038 e \sin 2 \bar{F},$">|; 

$key = q/displaystylefrac{r}{a};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="$\displaystyle \frac{r}{a}$">|; 

$key = q/1.60;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1943.png"
 ALT="$1.60$">|; 

$key = q/+20^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$+20^\circ $">|; 

$key = q/{displaymath}lambda=3.091simeq3^circ05'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img1263.png"
 ALT="\begin{displaymath}
\lambda =3.091\simeq 3^\circ 05'.
\end{displaymath}">|; 

$key = q/Deltabar{F}_M=bar{F}_M-bar{F}_{M,0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1625.png"
 ALT="$\Delta \bar{F}_M= \bar{F}_M-\bar{F}_{M 0}$">|; 

$key = q/r'slashr=aslashz;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2102.png"
 ALT="$r'/r = a/z$">|; 

$key = q/0.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="$0.2'$">|; 

$key = q/{displaymath}F=bar{F}+q=95.710-0.091=95.619simeq96^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2076.png"
 ALT="\begin{displaymath}
F = \bar{F} + q =95.710-0.091 = 95.619\simeq 96^\circ.
\end{displaymath}">|; 

$key = q/{{bf{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="${\bf z}$">|; 

$key = q/11^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="$11^\circ 34'$">|; 

$key = q/displaystyle-coslambda,sinepsilon,cosalpha_0,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$\displaystyle -\cos\lambda \sin \epsilon \cos\alpha_0,$">|; 

$key = q/bar{F}_M=63.131;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1567.png"
 ALT="$\bar{F}_M=63.131$">|; 

$key = q/48.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1145.png"
 ALT="$48.6'$">|; 

$key = q/deltaz=(e+e_S)slash(1-e^{2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2110.png"
 ALT="$\delta z = (e+e_S)/(1-e^{2})$">|; 

$key = q/bar{lambda}_0=280.458^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1187.png"
 ALT="$\bar{\lambda}_0 = 280.458^\circ$">|; 

$key = q/M_0=357.588^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1188.png"
 ALT="$M_0 = 357.588^\circ$">|; 

$key = q/+45^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="$+45^\circ 00'$">|; 

$key = q/displaystyleM+2,e,sinM+2,e^2,sin2M.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="$\displaystyle M + 2 e \sin M + 2 e^2 \sin 2M.$">|; 

$key = q/0.08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2043.png"
 ALT="$0.08'$">|; 

$key = q/{displaymath}frac{dbar{theta}}{dbar{mu}}=frac{bar{a}^{-1},cosbar{mu}+1}{1+2,bar{a}^{-1},cosbar{mu}+bar{a}^{-2}}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1947.png"
 ALT="\begin{displaymath}
\frac{d\bar{\theta}}{d\bar{\mu}} = \frac{\bar{a}^{-1} \cos\bar{\mu}+1}
{1 + 2 \bar{a}^{-1} \cos\bar{\mu} + \bar{a}^{-2}}.
\end{displaymath}">|; 

$key = q/+3.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$+3.9$">|; 

$key = q/300^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$300^\circ$">|; 

$key = q/y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="$y$">|; 

$key = q/+4^circ03';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$+4^\circ 03'$">|; 

$key = q/14.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1004.png"
 ALT="$14.0'$">|; 

$key = q/167.040;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="$167.040$">|; 

$key = q/displaystyle2,e,sinM+1.430,e^2,sin2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1200.png"
 ALT="$\displaystyle 2 e \sin M + 1.430 e^2 \sin 2M,$">|; 

$key = q/E;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$E$">|; 

$key = q/{displaymath}frac{x^2}{a^2}+frac{y^2}{b^2}=1,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="\begin{displaymath}
\frac{x^2}{a^2}+ \frac{y^2}{b^2} = 1,
\end{displaymath}">|; 

$key = q/038^circ01';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1407.png"
 ALT="$038^\circ01'$">|; 

$key = q/36.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1084.png"
 ALT="$36.6'$">|; 

$key = q/10';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$10'$">|; 

$key = q/{displaymath}t=t_0+355.1,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="\begin{displaymath}
t =t_0+355.1  {\rm JD},
\end{displaymath}">|; 

$key = q/{displaymath}a_1=M_Msimeq94^circ,~~~a_2=2bar{D}-M_M=2times184.850-94.072simeq276^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="503" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1538.png"
 ALT="\begin{displaymath}
a_1=M_M\simeq 94^\circ,&nbsp;&nbsp;&nbsp;a_2=2\bar{D}-M_M = 2\times 184.850-94.072\simeq 276^\circ,
\end{displaymath}">|; 

$key = q/r,cosT=a,(cosE-e);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="$r \cos T = a (\cos E - e)$">|; 

$key = q/-144.192;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1920.png"
 ALT="$-144.192$">|; 

$key = q/displaystylee,cosM-e^{,2},sin^2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1879.png"
 ALT="$\displaystyle e \cos M - e^{ 2} \sin^2 M,$">|; 

$key = q/{displaymath}deltatheta_-(114^circ)=3.853^circ,mbox{hspace{0.5cm}}bar{theta}(114hspace{0.5cm}}deltatheta_+(114^circ)=4.612^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="489" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1755.png"
 ALT="\begin{displaymath}
\delta\theta_-(114^\circ) = 3.853^\circ,\mbox{\hspace{0.5cm}...
... \mbox{\hspace{0.5cm}}\delta\theta_+(114^\circ) = 4.612^\circ.
\end{displaymath}">|; 

$key = q/CK=PL=2,e,a,sinM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="$CK = PL = 2 e a \sin M$">|; 

$key = q/80.108;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1895.png"
 ALT="$80.108$">|; 

$key = q/{displaymath}t=t_0+160+1.267slash0.61652137=t_0+162.1,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1938.png"
 ALT="\begin{displaymath}
t=t_0+160+1.267/0.61652137= t_0 + 162.1 {\rm JD},
\end{displaymath}">|; 

$key = q/(1slash4),e^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="$(1/4) e^2$">|; 

$key = q/displaystylebar{F}+q,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2027.png"
 ALT="$\displaystyle \bar{F} + q,$">|; 

$key = q/displaystyleq_5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1207.png"
 ALT="$\displaystyle q_5$">|; 

$key = q/35.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1054.png"
 ALT="$35.6'$">|; 

$key = q/353.814;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="$353.814$">|; 

$key = q/q_5=0.086^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1320.png"
 ALT="$q_5=0.086^\circ$">|; 

$key = q/ZYC;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ZYC$">|; 

$key = q/Fsimeqlambda-Omega;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1308.png"
 ALT="$F \simeq \lambda-\Omega$">|; 

$key = q/displaystyleE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="$\displaystyle E$">|; 

$key = q/delta_{M,0}=R_Eslasha_M=6371,{{rm{km}slash384,399,{{rm{km}=56.98';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1557.png"
 ALT="$\delta_{M 0} = R_E/a_M = 6371 {\rm km}/384,399 {\rm km}=56.98'$">|; 

$key = q/05.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1039.png"
 ALT="$05.2'$">|; 

$key = q/21.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img927.png"
 ALT="$21.4'$">|; 

$key = q/35^circ38';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$35^\circ38'$">|; 

$key = q/zeta_S=1.662times10^{-2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1912.png"
 ALT="$\zeta_S= 1.662\times 10^{-2}$">|; 

$key = q/28';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$28'$">|; 

$key = q/displaystylecosa,sinA,{{bf{e}+cosa,cosA,{{bf{n}+sina,{{bf{z},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle \cos a \sin A {\bf e} + \cos a \cos A {\bf n} + \sin a {\bf z},$">|; 

$key = q/Deltat~~~~~;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1191.png"
 ALT="$\Delta t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$">|; 

$key = q/-18^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="$-18^\circ 26'$">|; 

$key = q/+2.4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$+2.4$">|; 

$key = q/29^circ50';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="$29^\circ 50'$">|; 

$key = q/93.6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="$93.6$">|; 

$key = q/{displaymath}tsimeqt_0+533-1.455slash0.46157617simeqt_0+530,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1801.png"
 ALT="\begin{displaymath}
t\simeq t_0+533-1.455/0.46157617 \simeq t_0+ 530 {\rm JD}.
\end{displaymath}">|; 

$key = q/265.647;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$265.647$">|; 

$key = q/q_3=-0.631^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1318.png"
 ALT="$q_3=-0.631^\circ$">|; 

$key = q/48';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="$48'$">|; 

$key = q/e,a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="$e a$">|; 

$key = q/{displaymath}lambda=bar{lambda}_S+theta=273.055+35.027=308.082simeq308^circ5'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1934.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda}_S + \theta= 273.055+35.027= 308.082 \simeq 308^\circ 5'.
\end{displaymath}">|; 

$key = q/displaystylesinL,{{bf{p}+cosL,{{bf{m}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle \sin L {\bf p} + \cos L {\bf m}.$">|; 

$key = q/-0.262;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1773.png"
 ALT="$-0.262$">|; 

$key = q/PB;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1657.png"
 ALT="$PB$">|; 

$key = q/08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="$08'$">|; 

$key = q/114.449;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1484.png"
 ALT="$114.449$">|; 

$key = q/t-t_0=2,378,854.5-2,451,545.0=-72,690.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="$ t-t_0 = 2 378 854.5-2 451 545.0=-72 690.5$">|; 

$key = q/PiXDA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="$\Pi X D A$">|; 

$key = q/01.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img931.png"
 ALT="$01.6'$">|; 

$key = q/beta_{S}(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1604.png"
 ALT="$\beta_{S}(')$">|; 

$key = q/{displaymath}q_4(a_4)=-0.596^circ,~~q_5(a_5)=-0.119^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1513.png"
 ALT="\begin{displaymath}q_4(a_4)=-0.596^\circ,&nbsp;&nbsp;q_5(a_5)= -0.119^\circ.
\end{displaymath}">|; 

$key = q/190^circ22';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1363.png"
 ALT="$190^\circ 22'$">|; 

$key = q/51.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img924.png"
 ALT="$51.2'$">|; 

$key = q/{displaymath}h(mu,z)=left[z^2+2,a,z,cosmu+a^2right]^{-1slash2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img2104.png"
 ALT="\begin{displaymath}
h(\mu,z) = \left[z^2 + 2 a z \cos\mu+ a^2\right]^{-1/2}
\end{displaymath}">|; 

$key = q/{displaymath}Theta_-(-0.19)=-0.113,mbox{hspace{0.5cm}}Theta_+(-0.19)=-0.077,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1784.png"
 ALT="\begin{displaymath}
\Theta_-(-0.19) = -0.113, \mbox{\hspace{0.5cm}}
\Theta_+(-0.19) = -0.077,
\end{displaymath}">|; 

$key = q/13.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img974.png"
 ALT="$13.0'$">|; 

$key = q/33.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img982.png"
 ALT="$33.2'$">|; 

$key = q/VSV'S';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$VSV'S'$">|; 

$key = q/musimeq22^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2122.png"
 ALT="$\mu\simeq 22^\circ$">|; 

$key = q/{displaymath}z=(1-zeta)slash(1-zeta_S)=(1-4.913times10^{-2})slash(1+8.56times10^{-3})=0.9428.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1854.png"
 ALT="\begin{displaymath}
z= (1-\zeta)/(1-\zeta_S) = (1-4.913\times 10^{-2})/(1+8.56\times 10^{-3}) =
0.9428.
\end{displaymath}">|; 

$key = q/+0^circ09';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="$+0^\circ 09'$">|; 

$key = q/sin^{-1}(cosLslashsinepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\sin ^{-1} (\cos L/\sin \epsilon)$">|; 

$key = q/displaystylelambda_S-bar{lambda}-q,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1703.png"
 ALT="$\displaystyle \lambda_S - \bar{\lambda}-q,$">|; 

$key = q/23^circ41';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$23^\circ 41'$">|; 

$key = q/22.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img957.png"
 ALT="$22.4'$">|; 

$key = q/V';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$V'$">|; 

$key = q/F_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1216.png"
 ALT="$F_0$">|; 

$key = q/{displaymath}q(230^circ)=-0.592^circ,mbox{hspace{0.5cm}}zeta(230^circ)=-4.38times10^{-3},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1927.png"
 ALT="\begin{displaymath}
q(230^\circ)= -0.592^\circ,\mbox{\hspace{0.5cm}}\zeta(230^\circ)=-4.38\times 10^{-3},
\end{displaymath}">|; 

$key = q/textstyle=;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\textstyle =$">|; 

$key = q/R_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1547.png"
 ALT="$R_S$">|; 

$key = q/bar{F}=bar{lambda}-Omega;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1309.png"
 ALT="$\bar{F} = \bar{\lambda}-\Omega$">|; 

$key = q/SP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$SP$">|; 

$key = q/Z';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$Z'$">|; 

$key = q/{displaymath}a_5=2bar{F}_M=2times45.218simeq90^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1511.png"
 ALT="\begin{displaymath}
a_5=2\bar{F}_M = 2\times 45.218\simeq 90^\circ.
\end{displaymath}">|; 

$key = q/+10^circ06';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="$+10^\circ 06'$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q+theta=60.464+10.739-30.642=40.561simeq40^circ34'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1786.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda} + q + \theta= 60.464+10.739-30.642 = 40.561 \simeq 40^\circ 34'.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashfigv4.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img1646.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/figv4.eps}}
\end{figure}">|; 

$key = q/{displaymath}r''=(r^2+2,r,r',cosmu+r'^{,2})^{1slash2},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2018.png"
 ALT="\begin{displaymath}
r'' = (r^2 + 2 r r' \cos\mu+ r'^{ 2})^{1/2},
\end{displaymath}">|; 

$key = q/displaystyle0.422,e,sin(2tilde{D}-M),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1202.png"
 ALT="$\displaystyle 0.422 e \sin (2\tilde{D} - M),$">|; 

$key = q/42.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img971.png"
 ALT="$42.8'$">|; 

$key = q/{displaymath}{{bf{r}=cosdelta,cosalpha,{{bf{v}+cosdelta,sinalpha,{{bf{u}+sindelta,{{bf{p},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\begin{displaymath}
{\bf r} = \cos\delta \cos\alpha {\bf v} +
\cos\delta \sin\alpha {\bf u} + \sin\delta {\bf p},
\end{displaymath}">|; 

$key = q/+56^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="$+56^\circ 34'$">|; 

$key = q/+1.4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="$+1.4$">|; 

$key = q/033^circ39';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1411.png"
 ALT="$033^\circ 39'$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q+theta=196.501-0.091-5.921=190.489simeq190^circ29'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1837.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda} + q + \theta= 196.501-0.091-5.921=190.489 \simeq 190^\circ 29'.
\end{displaymath}">|; 

$key = q/CAequiva;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="$CA\equiv a$">|; 

$key = q/07';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="$07'$">|; 

$key = q/D=90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1447.png"
 ALT="$D = 90^\circ$">|; 

$key = q/mu=286.625^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2084.png"
 ALT="$\mu= 286.625^\circ$">|; 

$key = q/displaystylebar{F};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1195.png"
 ALT="$\displaystyle \bar{F}$">|; 

$key = q/q_4=-0.139^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1319.png"
 ALT="$q_4=-0.139^\circ$">|; 

$key = q/D=180.00^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1544.png"
 ALT="$D=180.00^\circ$">|; 

$key = q/19.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1172.png"
 ALT="$19.6'$">|; 

$key = q/theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1738.png"
 ALT="$\theta = \Theta_- \delta\theta_-+ \bar{\theta}
+ \Theta_+ \delta\theta_+$">|; 

$key = q/SP^2=SW^2+WP^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="$SP^2 = SW^2+ WP^2$">|; 

$key = q/{displaymath}deltatheta_-(253^circ)=-4.005^circ,mbox{hspace{0.5cm}}bar{theta}(25space{0.5cm}}deltatheta_+(253^circ)=-6.182^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="530" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1969.png"
 ALT="\begin{displaymath}
\delta\theta_-(253^\circ) = -4.005^\circ,\mbox{\hspace{0.5cm...
...\mbox{\hspace{0.5cm}}\delta\theta_+(253^\circ) = -6.182^\circ.
\end{displaymath}">|; 

$key = q/18.1^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1993.png"
 ALT="$18.1^\circ$">|; 

$key = q/displaystylebar{lambda}+q-lambda_S,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1880.png"
 ALT="$\displaystyle \bar{\lambda}+q-\lambda_S,$">|; 

$key = q/55.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1038.png"
 ALT="$55.0'$">|; 

$key = q/-88.708;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="$-88.708$">|; 

$key = q/+8^circ14';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$+8^\circ 14'$">|; 

$key = q/11.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img920.png"
 ALT="$11.2'$">|; 

$key = q/29.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1161.png"
 ALT="$29.2'$">|; 

$key = q/-46';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1412.png"
 ALT="$- 46'$">|; 

$key = q/90^circ-mu;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$90^\circ-\mu$">|; 

$key = q/+3.8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$+3.8$">|; 

$key = q/54.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1008.png"
 ALT="$54.0'$">|; 

$key = q/deltabeta_3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1639.png"
 ALT="$\delta\beta_3$">|; 

$key = q/-144.195;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1919.png"
 ALT="$-144.195$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{epsfilesslashumbra.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="678" HEIGHT="284" BORDER="0"
 SRC="|."$dir".q|img1563.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{epsfiles/umbra.eps}}
\end{figure}">|; 

$key = q/displaystyleTheta_-(xi),deltah_-+bar{h}+Theta_+(xi),delta,h_+,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2037.png"
 ALT="$\displaystyle \Theta_-(\xi) \delta h_-+ \bar{h}
+ \Theta_+(\xi) \delta h_+,$">|; 

$key = q/07.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1099.png"
 ALT="$07.2'$">|; 

$key = q/displaystyle{{bf{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle {\bf z}$">|; 

$key = q/19.712;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1490.png"
 ALT="$19.712$">|; 

$key = q/-30';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1405.png"
 ALT="$-30'$">|; 

$key = q/{displaymath}mu=bar{lambda}+q-bar{lambda}_S=314.268-16.974-44.602=252.692simeq253^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1968.png"
 ALT="\begin{displaymath}
\mu=\bar{\lambda}+q-\bar{\lambda}_S = 314.268-16.974-44.602= 252.692\simeq
253^\circ.
\end{displaymath}">|; 

$key = q/35.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1042.png"
 ALT="$35.2'$">|; 

$key = q/-29';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1416.png"
 ALT="$-29'$">|; 

$key = q/46.0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1985.png"
 ALT="$46.0^\circ$">|; 

$key = q/NPZS;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$NPZS$">|; 

$key = q/03.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img991.png"
 ALT="$03.6'$">|; 

$key = q/111.664;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1744.png"
 ALT="$111.664$">|; 

$key = q/{displaymath}beta_{M}=56.59'+deltabeta_1(M_M)+deltabeta_2(M_M)-deltabeta_3(M_S).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1593.png"
 ALT="\begin{displaymath}
\beta_{M} = 56.59' + \delta\beta_1(M_M)+\delta\beta_2 (M_M)-\delta\beta_3(M_S).
\end{displaymath}">|; 

$key = q/19.8^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2010.png"
 ALT="$19.8^\circ$">|; 

$key = q/L=+66^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$L=+66^\circ 34'$">|; 

$key = q/{displaymath}beta=h,beta_0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2021.png"
 ALT="\begin{displaymath}
\beta =h \beta_0,
\end{displaymath}">|; 

$key = q/-32';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1409.png"
 ALT="$-32'$">|; 

$key = q/+07';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1370.png"
 ALT="$+07'$">|; 

$key = q/19.7^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1996.png"
 ALT="$19.7^\circ$">|; 

$key = q/displaystyletheta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1712.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/08.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1135.png"
 ALT="$08.4'$">|; 

$key = q/36.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1072.png"
 ALT="$36.2'$">|; 

$key = q/266.549;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2135.png"
 ALT="$266.549$">|; 

$key = q/musimeq208^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2078.png"
 ALT="$\mu\simeq 208^\circ$">|; 

$key = q/Deltabar{lambda}(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1183.png"
 ALT="$\Delta\bar{\lambda}(^\circ)$">|; 

$key = q/displaystylebeta_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2028.png"
 ALT="$\displaystyle \beta_0$">|; 

$key = q/50.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="$50.0'$">|; 

$key = q/+65^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$+65^\circ $">|; 

$key = q/F_0(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1422.png"
 ALT="$ F_0(^\circ)$">|; 

$key = q/RSPequivT;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="$RSP\equiv T$">|; 

$key = q/25.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1053.png"
 ALT="$25.6'$">|; 

$key = q/mu=lambda_S-bar{lambda}-q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1726.png"
 ALT="$\mu = \lambda_S-\bar{\lambda}-q$">|; 

$key = q/{displaymath}frac{dlambda}{dt}simeqn+left(frac{bar{a},cosbar{mu}+1}{1+2,bar{a},cosbar{mu}+bar{a}^2}right)(n_S-n).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1811.png"
 ALT="\begin{displaymath}
\frac{d\lambda}{dt} \simeq n + \left(\frac{\bar{a}  \cos\bar{\mu}+1}{1+2 \bar{a} \cos\bar{\mu}+\bar{a}^2}\right) (n_S-n).
\end{displaymath}">|; 

$key = q/deltalambda=YE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1348.png"
 ALT="$\delta\lambda = YE$">|; 

$key = q/a_3=bar{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1472.png"
 ALT="$a_3=\bar{D}$">|; 

$key = q/26.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1065.png"
 ALT="$26.0'$">|; 

$key = q/647.268;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1962.png"
 ALT="$647.268$">|; 

$key = q/t=2,453,495.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="$t = 2 453 495.5$">|; 

$key = q/Deltat=2453174.1-2451545.0=1629.1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1478.png"
 ALT="$\Delta t = 2453174.1-2451545.0=1629.1$">|; 

$key = q/31.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img934.png"
 ALT="$31.6'$">|; 

$key = q/{displaymath}a_1=Msimeq58^circ,~~~a_2=2tilde{D}-M=2times314.281-58.185=570.377simeq210^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1257.png"
 ALT="\begin{displaymath}
a_1=M\simeq 58^\circ,&nbsp;&nbsp;&nbsp;a_2=2\tilde{D}-M = 2\times 314.281-58.185=570.377\simeq 210^\circ,
\end{displaymath}">|; 

$key = q/{displaymath}z=(1-zeta)slash(1-zeta_S)=(1+4.838times10^{-2})slash(1+8.56times10^{-3})=1.0395.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1831.png"
 ALT="\begin{displaymath}
z= (1-\zeta)/(1-\zeta_S) = (1+4.838\times 10^{-2})/(1+8.56\times 10^{-3}) =
1.0395.
\end{displaymath}">|; 

$key = q/+88^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="$+88^\circ 26'$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q=42.961+1.641=44.602simeq44^circ36'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="\begin{displaymath}
\lambda =\bar{\lambda} + q =42.961+ 1.641=44.602\simeq 44^\circ36'.
\end{displaymath}">|; 

$key = q/{displaymath}mu=lambda_S-bar{lambda}-q=44.602-297.661+7.345=114.286simeq114^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1754.png"
 ALT="\begin{displaymath}
\mu=\lambda_S - \bar{\lambda}-q = 44.602-297.661 + 7.345= 114.286\simeq
114^\circ,
\end{displaymath}">|; 

$key = q/+6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$+6$">|; 

$key = q/displaystyle-sina,sinA,{{bf{e}-sina,cosA,{{bf{n}-cosa,{{bf{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle -\sin a \sin A {\bf e}-\sin a \cos A {\bf n} -\cos a {\bf z}$">|; 

$key = q/bar{F}_0=105.253^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1982.png"
 ALT="$\bar{F}_0 =105.253^\circ$">|; 

$key = q/q=-7.345^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2052.png"
 ALT="$q= -7.345^\circ$">|; 

$key = q/0.801;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1897.png"
 ALT="$0.801$">|; 

$key = q/18.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1130.png"
 ALT="$18.2'$">|; 

$key = q/{displaymath}lambda=varpi+T,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="\begin{displaymath}
\lambda = \varpi + T,
\end{displaymath}">|; 

$key = q/F=bar{F}+q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2048.png"
 ALT="$F=\bar{F} + q$">|; 

$key = q/17^circ58';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="$17^\circ 58'$">|; 

$key = q/34.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1024.png"
 ALT="$34.6'$">|; 

$key = q/-47.166;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1771.png"
 ALT="$-47.166$">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=-0.071times0.353-5.551-0.759times0.405=-5.883^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1859.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
...+ = -0.071\times 0.353-5.551-0.759\times 0.405 =- 5.883^\circ.
\end{displaymath}">|; 

$key = q/r_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1548.png"
 ALT="$r_S$">|; 

$key = q/displaystyleh(mu,bar{z})equivleft[bar{z}^2+2,a,bar{z},cosmu+a^2right]^{-1slash2},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2108.png"
 ALT="$\displaystyle h(\mu,\bar{z})\equiv\left[\bar{z}^2 + 2 a \bar{z} \cos\mu+ a^2\right]^{-1/2},$">|; 

$key = q/|beta_{syz}|<rho_U-rho_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1577.png"
 ALT="$\vert\beta_{syz}\vert &lt; \rho_U-\rho_M$">|; 

$key = q/-13^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="$-13^\circ 26'$">|; 

$key = q/X;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$X$">|; 

$key = q/mu=111.7^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1977.png"
 ALT="$\mu=111.7^\circ$">|; 

$key = q/83.125;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1818.png"
 ALT="$83.125$">|; 

$key = q/{displaymath}frac{x'^{,2}}{a^2}+frac{y'^{,2}}{a^2}=1.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="\begin{displaymath}
\frac{x'^{ 2}}{a^2} + \frac{y'^{ 2}}{a^2} = 1.
\end{displaymath}">|; 

$key = q/Pi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\Pi $">|; 

$key = q/231.360;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1486.png"
 ALT="$231.360$">|; 

$key = q/{displaymath}q_4(a_4)=-0.139^circ,~~q_5(a_5)=0.086^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1261.png"
 ALT="\begin{displaymath}q_4(a_4)=-0.139^\circ,&nbsp;&nbsp;q_5(a_5)= 0.086^\circ.
\end{displaymath}">|; 

$key = q/06.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1063.png"
 ALT="$06.0'$">|; 

$key = q/02';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="$02'$">|; 

$key = q/DeltaM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="$\Delta M$">|; 

$key = q/breve{n}(^circslash{{rm{day});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1419.png"
 ALT="$\breve{n}(^\circ/{\rm day})$">|; 

$key = q/-850.423;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1923.png"
 ALT="$-850.423$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashmoon.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="338" BORDER="0"
 SRC="|."$dir".q|img1299.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/moon.eps}}
\end{figure}">|; 

$key = q/29.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1173.png"
 ALT="$29.6'$">|; 

$key = q/+1.7;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$+1.7$">|; 

$key = q/33';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="$33'$">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.00109-1.0395)slash0.06512simeq-0.59.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1834.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.00109-1.0395)/0.06512 \simeq -0.59.
\end{displaymath}">|; 

$key = q/22^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$22^\circ 34'$">|; 

$key = q/3.3692;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2147.png"
 ALT="$3.3692$">|; 

$key = q/234.4^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1839.png"
 ALT="$234.4^\circ$">|; 

$key = q/50.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="$50.4'$">|; 

$key = q/NGN';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1300.png"
 ALT="$NGN'$">|; 

$key = q/displaystyleq_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1205.png"
 ALT="$\displaystyle q_4$">|; 

$key = q/M_Ssimeq120^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1740.png"
 ALT="$M_S\simeq 120^\circ$">|; 

$key = q/-2^circ36';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$-2^\circ 36'$">|; 

$key = q/deltah_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2047.png"
 ALT="$\delta h_+$">|; 

$key = q/607.938;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2060.png"
 ALT="$607.938$">|; 

$key = q/{displaymath}z=(1-zeta)slash(1-zeta_S)=(1-6.912times10^{-2})slash(1+8.56times10^{-3})=0.9230.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1756.png"
 ALT="\begin{displaymath}
z= (1-\zeta)/(1-\zeta_S) = (1-6.912\times 10^{-2})/(1+8.56\times 10^{-3}) =
0.9230.
\end{displaymath}">|; 

$key = q/{displaymath}lambda=bar{lambda}+q=273.259-0.204=273.055simeq273^circ03'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="\begin{displaymath}
\lambda =\bar{\lambda} + q = 273.259 - 0.204=273.055\simeq 273^\circ03'.
\end{displaymath}">|; 

$key = q/+25^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="$+25^\circ 00'$">|; 

$key = q/+40^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="$+40^\circ 00'$">|; 

$key = q/{displaymath}q_1(a_1)=6.239^circ,~~q_2(a_2)=-1.320^circ,~~q_3(a_3)=0.119^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1541.png"
 ALT="\begin{displaymath}
q_1(a_1)=6.239^\circ,&nbsp;&nbsp;q_2(a_2)= -1.320^\circ,&nbsp;&nbsp;q_3(a_3) = 0.119^\circ,
\end{displaymath}">|; 

$key = q/Q';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$Q'$">|; 

$key = q/12^h35^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$12^h35^m$">|; 

$key = q/DYB;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$DYB$">|; 

$key = q/626.549;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2134.png"
 ALT="$626.549$">|; 

$key = q/46';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="$46'$">|; 

$key = q/bar{alpha};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="$\bar{\alpha}$">|; 

$key = q/+15^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="$+15^\circ$">|; 

$key = q/49';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="$49'$">|; 

$key = q/-24';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1398.png"
 ALT="$-24'$">|; 

$key = q/326^circ23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$326^\circ 23'$">|; 

$key = q/dbar{mu}slashdt=n_S-n;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1810.png"
 ALT="$d\bar{\mu}/dt = n_S-n$">|; 

$key = q/29.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1179.png"
 ALT="$29.8'$">|; 

$key = q/{displaymath}beta=frac{v}{r''},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img2015.png"
 ALT="\begin{displaymath}
\beta = \frac{v}{r''},
\end{displaymath}">|; 

$key = q/46.5^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1987.png"
 ALT="$46.5^\circ$">|; 

$key = q/{displaymath}F=bar{F}_M+q_1+q_2+q_3+q_{4'}+q_5,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1565.png"
 ALT="\begin{displaymath}
F = \bar{F}_M + q_1+q_2+q_3+q_{4'}+q_5,
\end{displaymath}">|; 

$key = q/055^circ11';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1400.png"
 ALT="$055^\circ 11'$">|; 

$key = q/52.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img960.png"
 ALT="$52.4'$">|; 

$key = q/deltaa=41.050,(1-0.00953)simeq41';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1342.png"
 ALT="$\delta a = 41.050 (1-0.00953) \simeq 41'$">|; 

$key = q/bar{F}_0=93.284^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1429.png"
 ALT="$\bar{F}_0 = 93.284^\circ$">|; 

$key = q/-6.615;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1281.png"
 ALT="$-6.615$">|; 

$key = q/bar{theta}~~~~;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1867.png"
 ALT="$\bar{\theta}&nbsp;&nbsp;&nbsp;&nbsp;$">|; 

$key = q/51.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img942.png"
 ALT="$51.8'$">|; 

$key = q/Deltat=t-t_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$\Delta t = t-t_0$">|; 

$key = q/displaystyle-sinalpha_0,{{bf{v}+cosepsilon,cosalpha_0,{{bf{s}-sinepsilon,cosalpha_0,{{bf{q},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle -\sin \alpha_0 {\bf v} + \cos\epsilon \cos \alpha_0 {\bf s} - \sin\epsilon \cos \alpha_0 {\bf q},$">|; 

$key = q/mu=208.192^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2070.png"
 ALT="$\mu= 208.192^\circ$">|; 

$key = q/{{bf{q};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="${\bf q}$">|; 

$key = q/{displaymath}Theta_-(0.72)=0.101,mbox{hspace{0.5cm}}Theta_+(0.72)=0.619,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1760.png"
 ALT="\begin{displaymath}
\Theta_-(0.72) = 0.101, \mbox{\hspace{0.5cm}}\Theta_+(0.72) = 0.619,
\end{displaymath}">|; 

$key = q/displaystylebar{F}_0+breve{n},(t-t_0),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1196.png"
 ALT="$\displaystyle \bar{F}_0 + \breve {n} (t-t_0),$">|; 

$key = q/+68^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="$+68^\circ 26'$">|; 

$key = q/58.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1140.png"
 ALT="$58.4'$">|; 

$key = q/+41^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="$+41^\circ 34'$">|; 

$key = q/bar{z}=(1+e,e_S)slash(1-e^{,2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1884.png"
 ALT="$\bar{z} = (1+e e_S)/(1-e^{ 2})$">|; 

$key = q/displaystyle0.211,e,(sin2tilde{D}-0.066,sintilde{D}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1204.png"
 ALT="$\displaystyle 0.211 e (\sin 2\tilde{D} - 0.066 \sin \tilde{D}),$">|; 

$key = q/337.132;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1255.png"
 ALT="$337.132$">|; 

$key = q/44.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1019.png"
 ALT="$44.4'$">|; 

$key = q/20.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="$20.4'$">|; 

$key = q/34.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1030.png"
 ALT="$34.8'$">|; 

$key = q/20.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="$20.8'$">|; 

$key = q/53.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img990.png"
 ALT="$53.4'$">|; 

$key = q/100,zeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1190.png"
 ALT="$100 \zeta$">|; 

$key = q/23.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img981.png"
 ALT="$23.2'$">|; 

$key = q/03.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img997.png"
 ALT="$03.8'$">|; 

$key = q/26.202;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2058.png"
 ALT="$26.202$">|; 

$key = q/displaystyle-cosA,sinepsilon,cos(alpha-t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$\displaystyle -\cos A \sin\epsilon \cos(\alpha-t)$">|; 

$key = q/deltaz=(e+e_S)slash(1-e_S^{,2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1716.png"
 ALT="$\delta z = (e+e_S)/(1-e_S^{ 2})$">|; 

$key = q/20^circ47';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$20^\circ 47'$">|; 

$key = q/26.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1071.png"
 ALT="$26.2'$">|; 

$key = q/q_1(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1430.png"
 ALT="$q_1(^\circ)$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere2.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere2.eps}}
\end{figure}">|; 

$key = q/1.8467;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2149.png"
 ALT="$1.8467$">|; 

$key = q/theta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="$\theta$">|; 

$key = q/0.5-sin^{-1}(cosLslashsinepsilon)slash180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$0.5-\sin^{-1}(\cos L/\sin \epsilon)/180^\circ$">|; 

$key = q/229.577;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1925.png"
 ALT="$229.577$">|; 

$key = q/M_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1211.png"
 ALT="$M_S$">|; 

$key = q/326^circ23'-126^circ32'=199^circ51';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$326^\circ23'-126^\circ 32' = 199^\circ 51'$">|; 

$key = q/{displaymath}D=bar{D}+q_1+q_2+q_3+q_4+q_5=357.813+0.101+0.070-0.045-0.596-0.119simeq357.22^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="626" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1514.png"
 ALT="\begin{displaymath}
D = \bar{D} + q_1+q_2+q_3+q_4+q_5=357.813+0.101+0.070-0.045-0.596-0.119\simeq
357.22^\circ.
\end{displaymath}">|; 

$key = q/mu;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$\mu$">|; 

$key = q/displaystylemu;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1702.png"
 ALT="$\displaystyle \mu$">|; 

$key = q/883.229;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1503.png"
 ALT="$883.229$">|; 

$key = q/N;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$N$">|; 

$key = q/-180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="$-180^\circ$">|; 

$key = q/33.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img976.png"
 ALT="$33.0'$">|; 

$key = q/{displaymath}cost_h=-tanL,tandelta.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="\begin{displaymath}
\cos t_h = - \tan L \tan\delta.
\end{displaymath}">|; 

$key = q/murightarrow360^circ-mu;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$\mu\rightarrow 360^\circ-\mu$">|; 

$key = q/57.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1098.png"
 ALT="$57.0'$">|; 

$key = q/Theta_-=-0.469;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2071.png"
 ALT="$\Theta_-=-0.469$">|; 

$key = q/{displaymath}frac{partial{{bf{r}}{partiallambda}=-sinlambda,{{bf{v}+coslambda,{{bf{s}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="\begin{displaymath}
\frac{\partial {\bf r}}{\partial \lambda} = -\sin\lambda {\bf v} + \cos\lambda {\bf s}
\end{displaymath}">|; 

$key = q/a_M=384,399;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1333.png"
 ALT="$a_M=384,399$">|; 

$key = q/11.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img914.png"
 ALT="$11.0'$">|; 

$key = q/6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1313.png"
 ALT="$6'$">|; 

$key = q/displaystyletanalpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle \tan\alpha$">|; 

$key = q/23.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img993.png"
 ALT="$23.6'$">|; 

$key = q/52.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img966.png"
 ALT="$52.6'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere1.eps}}
\end{figure}">|; 

$key = q/270^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$270^\circ$">|; 

$key = q/16.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1076.png"
 ALT="$16.4'$">|; 

$key = q/lambda=60^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$\lambda=60^\circ$">|; 

$key = q/displaystylesini,sinF,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2029.png"
 ALT="$\displaystyle \sin i \sin F,$">|; 

$key = q/13.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img998.png"
 ALT="$13.8'$">|; 

$key = q/displaystyleTheta_-(xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1693.png"
 ALT="$\displaystyle \Theta_-(\xi)$">|; 

$key = q/q';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1661.png"
 ALT="$q'$">|; 

$key = q/47.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1115.png"
 ALT="$47.6'$">|; 

$key = q/displaystylebar{lambda};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="$\displaystyle \bar{\lambda}$">|; 

$key = q/{{bf{z}cdot{{bf{q}<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="${\bf z}\cdot{\bf q} &lt;0$">|; 

$key = q/sinbeta=sini,sinF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1307.png"
 ALT="$\sin\beta = \sin i \sin F$">|; 

$key = q/{displaymath}a_5=2bar{F}=2times337.132=674.264simeq314^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1259.png"
 ALT="\begin{displaymath}
a_5=2\bar{F} = 2\times 337.132=674.264\simeq 314^\circ.
\end{displaymath}">|; 

$key = q/{displaymath}q_4(a_4)=0.017^circ,~~q_5(a_5)=-0.021^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1293.png"
 ALT="\begin{displaymath}q_4(a_4)=0.017^\circ,&nbsp;&nbsp;q_5(a_5)= -0.021^\circ.
\end{displaymath}">|; 

$key = q/ZW=XL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="$ZW=XL$">|; 

$key = q/t=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$t=0$">|; 

$key = q/31.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img916.png"
 ALT="$31.0'$">|; 

$key = q/{displaymath}t=t_0+183-0.294slash0.461557617=t_0+182.4,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1796.png"
 ALT="\begin{displaymath}
t=t_0 +183-0.294/0.461557617=t_0+182.4  {\rm JD},
\end{displaymath}">|; 

$key = q/L=90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$L=90^\circ$">|; 

$key = q/56.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1092.png"
 ALT="$56.8'$">|; 

$key = q/+epsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$+\epsilon$">|; 

$key = q/r;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="$r$">|; 

$key = q/293.250;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1242.png"
 ALT="$293.250$">|; 

$key = q/5.202873;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$5.202873$">|; 

$key = q/1.000000;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="$1.000000$">|; 

$key = q/40.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="$40.2'$">|; 

$key = q/Pi'PA';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1647.png"
 ALT="$\Pi'PA'$">|; 

$key = q/t-t_0=1950.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1231.png"
 ALT="$t-t_0=1950.5$">|; 

$key = q/lambda_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1210.png"
 ALT="$\lambda_S$">|; 

$key = q/6.532;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1245.png"
 ALT="$6.532$">|; 

$key = q/z=(1-zeta)slash(1-zeta_S);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1730.png"
 ALT="$z = (1-\zeta)/(1-\zeta_S)$">|; 

$key = q/+45^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="$+45^\circ$">|; 

$key = q/+90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$+90^\circ$">|; 

$key = q/117.585;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1495.png"
 ALT="$117.585$">|; 

$key = q/displaystylesini,sinF.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1312.png"
 ALT="$\displaystyle \sin i \sin F.$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{118^circ26'{&{020^circ25'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="973" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $118^\circ 26'$&amp; $020^\circ 25'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/M_Ssimeq354^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1763.png"
 ALT="$M_S\simeq 354^\circ$">|; 

$key = q/10^circ08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$10^\circ 08'$">|; 

$key = q/bar{D}(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1479.png"
 ALT="$ \bar{D}(^\circ)$">|; 

$key = q/355.460;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="$355.460$">|; 

$key = q/+85^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="$+85^\circ 00'$">|; 

$key = q/h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="$h$">|; 

$key = q/displaystyleTheta_-(xi),deltatheta_-+bar{theta}+Theta_+(xi),deltatheta_+,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1713.png"
 ALT="$\displaystyle \Theta_-(\xi) \delta\theta_-+ \bar{\theta}
+ \Theta_+(\xi) \delta\theta_+,$">|; 

$key = q/mu=178.900^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1940.png"
 ALT="$\mu=178.900^\circ$">|; 

$key = q/PiPDA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="$\Pi P D A$">|; 

$key = q/bar{z}=1.00184;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1757.png"
 ALT="$\bar{z}= 1.00184$">|; 

$key = q/04.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1021.png"
 ALT="$04.6'$">|; 

$key = q/{displaymath}thetasimeqbar{theta}=tan^{-1}left(frac{sinbar{mu}}{bar{a}^{-1}+cosbar{mu}}right),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1944.png"
 ALT="\begin{displaymath}
\theta\simeq \bar{\theta} = \tan^{-1}\left(\frac{\sin \bar{\mu}}{\bar{a}^{-1}+\cos\bar{\mu}}\right),
\end{displaymath}">|; 

$key = q/24.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1017.png"
 ALT="$24.4'$">|; 

$key = q/displaystyleleft(frac{{{bf{r}cdot{{bf{s}}{{{bf{r}cdot{{bf{v}}right),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \left(\frac{{\bf r}\cdot{\bf s}}{{\bf r}\cdot {\bf v}}\right),$">|; 

$key = q/06.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1075.png"
 ALT="$06.4'$">|; 

$key = q/+10^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="$+10^\circ 00'$">|; 

$key = q/+48^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="$+48^\circ 26'$">|; 

$key = q/1.5';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2041.png"
 ALT="$1.5'$">|; 

$key = q/mu=bar{lambda}+q-lambda_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1889.png"
 ALT="$\mu = \bar{\lambda}+q-\lambda_S$">|; 

$key = q/5.2%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1615.png"
 ALT="$5.2\%$">|; 

$key = q/16^circ15';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$16^\circ 15'$">|; 

$key = q/deltaz;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1718.png"
 ALT="$\delta z$">|; 

$key = q/07.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1093.png"
 ALT="$07.0'$">|; 

$key = q/{figure}{epsfysize{=3.in{centerline{epsffile{epsfilesslashsun.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="625" HEIGHT="337" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="\begin{figure}
\epsfysize =3.in
\centerline{\epsffile{epsfiles/sun.eps}}
\end{figure}">|; 

$key = q/z_{{rm{max}=bar{z}+deltaz;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1677.png"
 ALT="$z_{\rm max} = \bar{z}+\delta z$">|; 

$key = q/59.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1176.png"
 ALT="$59.6'$">|; 

$key = q/39^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$39^\circ00'$">|; 

$key = q/{displaymath}mu=lambda_S-bar{lambda}-q=44.602-115.416-2.561=-73.375simeq287^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="472" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1852.png"
 ALT="\begin{displaymath}
\mu=\lambda_S - \bar{\lambda}-q = 44.602-115.416 -2.561= -73.375\simeq
287^\circ,
\end{displaymath}">|; 

$key = q/{displaymath}D=bar{D}+q_1+q_2+q_3+q_4+q_5=184.850+6.239-1.320+0.119-1.896-0.097simeq187.895^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="635" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1543.png"
 ALT="\begin{displaymath}
D = \bar{D} + q_1+q_2+q_3+q_4+q_5=184.850+6.239-1.320+0.119-1.896-0.097\simeq
187.895^\circ.
\end{displaymath}">|; 

$key = q/bar{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1465.png"
 ALT="$\bar{D}$">|; 

$key = q/0.006777;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="$0.006777$">|; 

$key = q/49.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1163.png"
 ALT="$49.2'$">|; 

$key = q/+81^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="$+81^\circ 34'$">|; 

$key = q/CQ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="$CQ$">|; 

$key = q/lambda=180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="$\lambda = 180^\circ$">|; 

$key = q/44';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="$44'$">|; 

$key = q/KS=2,e,a,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="$KS=2 e a \cos M$">|; 

$key = q/displaystyle-(0.051,e_M+2,e_S),sinM_S-(5slash4),e_S^{,2},sin2M_S,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1455.png"
 ALT="$\displaystyle -(0.051 e_M+2 e_S) \sin M_S - (5/4) e_S^{ 2} \sin 2 M_S,$">|; 

$key = q/24.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1011.png"
 ALT="$24.2'$">|; 

$key = q/06.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1081.png"
 ALT="$06.6'$">|; 

$key = q/Theta_-=0.071;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2085.png"
 ALT="$\Theta_-=0.071$">|; 

$key = q/09';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="$09'$">|; 

$key = q/Theta_+=0.619;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2055.png"
 ALT="$\Theta_+ = 0.619$">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.04774-0.8873)slash0.23216simeq0.69.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1973.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.04774-0.8873)/0.23216 \simeq 0.69.
\end{displaymath}">|; 

$key = q/displaystylez;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1708.png"
 ALT="$\displaystyle z$">|; 

$key = q/7.7%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1612.png"
 ALT="$7.7\%$">|; 

$key = q/30.130;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2088.png"
 ALT="$30.130$">|; 

$key = q/0.03348152;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="$0.03348152$">|; 

$key = q/298.820;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1241.png"
 ALT="$298.820$">|; 

$key = q/|beta_{syz}|<beta_{Mt};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1587.png"
 ALT="$\vert\beta_{syz}\vert&lt; \beta_{Mt}$">|; 

$key = q/bar{F}_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1464.png"
 ALT="$\bar{F}_M$">|; 

$key = q/t-t_0=-72,690.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1264.png"
 ALT="$t-t_0=-72 690.5$">|; 

$key = q/40';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="$40'$">|; 

$key = q/deltatheta_pm(360^circ-mu)=-deltatheta_pm(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1728.png"
 ALT="$\delta\theta_\pm(360^\circ - \mu) =-\delta\theta_\pm(\mu)$">|; 

$key = q/14^circ36';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="$14^\circ36'$">|; 

$key = q/deltaa=YF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1347.png"
 ALT="$\delta a = YF$">|; 

$key = q/50';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="$50'$">|; 

$key = q/33.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img988.png"
 ALT="$33.4'$">|; 

$key = q/+33';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1384.png"
 ALT="$+33'$">|; 

$key = q/+63^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="$+63^\circ 26'$">|; 

$key = q/19.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1166.png"
 ALT="$19.4'$">|; 

$key = q/rslashr'=(aslasha'),z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1666.png"
 ALT="$r/r' = (a/a') z$">|; 

$key = q/displaystyleM_{0}+tilde{n},(t-t_0),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1877.png"
 ALT="$\displaystyle M_{0} +\tilde{n} (t-t_0),$">|; 

$key = q/displaystyle2,e_M,sinM_M+1.430,e^2,sin2M_M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1452.png"
 ALT="$\displaystyle 2 e_M \sin M_M + 1.430 e^2 \sin 2M_M,$">|; 

$key = q/02.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img943.png"
 ALT="$02.0'$">|; 

$key = q/rho_U;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2162.png"
 ALT="$\rho_U$">|; 

$key = q/1slash24;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$1/24$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{159^circ26'{&{339^circ26'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="934" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $159^\circ 26'$&amp; $339^\circ 26'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/t=2,448,784.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="$t=2 448 784.5$">|; 

$key = q/{displaymath}rsimeqa_M,(1-e,cosM),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1327.png"
 ALT="\begin{displaymath}
r \simeq a_M (1 - e \cos M),
\end{displaymath}">|; 

$key = q/29.53;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1476.png"
 ALT="$29.53$">|; 

$key = q/+31^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="$+31^\circ 34'$">|; 

$key = q/145^circ55';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1388.png"
 ALT="$145^\circ 55'$">|; 

$key = q/displaystyle-sinlambda,cosA,{{bf{v}times{{bf{e}cdot{{bf{r}+sinlambda,sinA,{{bf{v}times{{bf{n}cdot{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$\displaystyle -\sin\lambda
 \cos A {\bf v}\times{\bf e}\cdot{\bf r}+\sin\lambda \sin A {\bf v}\times{\bf n}\cdot{\bf r}$">|; 

$key = q/{displaymath}M=left(frac{2pi}{tau}right),(t-t_ast){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="\begin{displaymath}
M = \left(\frac{2\pi}{\tau}\right) (t-t_\ast)
\end{displaymath}">|; 

$key = q/GP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2017.png"
 ALT="$GP$">|; 

$key = q/36.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1078.png"
 ALT="$36.4'$">|; 

$key = q/Theta_pm(xi)=-Theta_mp(-xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1863.png"
 ALT="$\Theta_\pm (\xi) = - \Theta_\mp (-\xi)$">|; 

$key = q/56.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1080.png"
 ALT="$56.4'$">|; 

$key = q/bar{F}_0=296.482^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1874.png"
 ALT="$\bar{F}_0 =296.482^\circ$">|; 

$key = q/r'';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2016.png"
 ALT="$r''$">|; 

$key = q/55.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1050.png"
 ALT="$55.4'$">|; 

$key = q/|beta_{syz}|(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1607.png"
 ALT="$\vert\beta_{syz}\vert(')$">|; 

$key = q/{displaymath}h=Theta_-,deltah_-+bar{h}+Theta_+,deltah_+=0.107times0.184+1.037+0.583times0.272=1.215.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2140.png"
 ALT="\begin{displaymath}
h = \Theta_- \delta h_- + \bar{h}+\Theta_+ \delta h_+ = 0.107\times 0.184+1.037+0.583\times 0.272= 1.215.
\end{displaymath}">|; 

$key = q/2bar{F}_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1633.png"
 ALT="$2\bar{F}_M$">|; 

$key = q/displaystyleM+e,sinM+(1slash2),e^2,sin2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="$\displaystyle M + e \sin M + (1/2) e^2 \sin 2M,$">|; 

$key = q/q_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1438.png"
 ALT="$q_2$">|; 

$key = q/58.185;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1254.png"
 ALT="$58.185$">|; 

$key = q/lambda=210^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1357.png"
 ALT="$\lambda=210^\circ$">|; 

$key = q/1^circ32';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2082.png"
 ALT="$1^\circ 32'$">|; 

$key = q/19.475;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1285.png"
 ALT="$19.475$">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=0.101times3.853+39.209+0.619times4.612=42.453^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1761.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
...+ = 0.101\times 3.853+39.209+0.619\times 4.612 = 42.453^\circ.
\end{displaymath}">|; 

$key = q/delta(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1443.png"
 ALT="$\delta(')$">|; 

$key = q/displaystyle{{bf{r}cdot{{bf{p},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle {\bf r}\cdot {\bf p},$">|; 

$key = q/39.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1174.png"
 ALT="$39.6'$">|; 

$key = q/+8^circ49';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="$+8^\circ 49'$">|; 

$key = q/30.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="$30.2'$">|; 

$key = q/NG'P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2101.png"
 ALT="$NG'P$">|; 

$key = q/-324.983;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1765.png"
 ALT="$-324.983$">|; 

$key = q/bar{h}(360^circ-mu)=bar{h}(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2050.png"
 ALT="$\bar{h}(360^\circ - \mu) = \bar{h}(\mu)$">|; 

$key = q/31.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img922.png"
 ALT="$31.2'$">|; 

$key = q/{figure}{epsfysize{=5.5in{centerline{epsffile{epsfilesslashecliptic1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="757" HEIGHT="517" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="\begin{figure}
\epsfysize =5.5in
\centerline{\epsffile{epsfiles/ecliptic1.eps}}
\end{figure}">|; 

$key = q/33.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1000.png"
 ALT="$33.8'$">|; 

$key = q/+53^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="$+53^\circ 26'$">|; 

$key = q/{displaymath}|beta_{syz}|<delta_M+rho_M-rho_S,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1583.png"
 ALT="\begin{displaymath}
\vert\beta_{syz}\vert &lt; \delta_M + \rho_M - \rho_S,
\end{displaymath}">|; 

$key = q/{displaymath}xi=frac{bar{z}-z}{deltaz}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1680.png"
 ALT="\begin{displaymath}
\xi = \frac{\bar{z}-z}{\delta z}.
\end{displaymath}">|; 

$key = q/1.60216872;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="$1.60216872$">|; 

$key = q/59.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1182.png"
 ALT="$59.8'$">|; 

$key = q/^ast;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="$^\ast$">|; 

$key = q/111.637;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2057.png"
 ALT="$111.637$">|; 

$key = q/1.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1721.png"
 ALT="$1.6'$">|; 

$key = q/q_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1219.png"
 ALT="$q_1$">|; 

$key = q/30.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="$30.0'$">|; 

$key = q/0leqeleq1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="$0\leq e\leq 1$">|; 

$key = q/15^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$15^\circ$">|; 

$key = q/54.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1020.png"
 ALT="$54.4'$">|; 

$key = q/04^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="$04^\circ 34'$">|; 

$key = q/95.710;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2075.png"
 ALT="$95.710$">|; 

$key = q/displaystylebar{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1450.png"
 ALT="$\displaystyle \bar{D}$">|; 

$key = q/657.661;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1749.png"
 ALT="$657.661$">|; 

$key = q/+3.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="$+3.5$">|; 

$key = q/-4^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="$-4^\circ 34'$">|; 

$key = q/17.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1100.png"
 ALT="$17.2'$">|; 

$key = q/+71^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="$+71^\circ 34'$">|; 

$key = q/xi<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1735.png"
 ALT="$\xi&lt;0$">|; 

$key = q/176^circ40';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1378.png"
 ALT="$176^\circ 40'$">|; 

$key = q/12.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img962.png"
 ALT="$12.6'$">|; 

$key = q/0.262;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1748.png"
 ALT="$0.262$">|; 

$key = q/M_0(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1421.png"
 ALT="$M_0(^\circ)$">|; 

$key = q/cosmurightarrowcosmu;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$\cos\mu\rightarrow \cos\mu$">|; 

$key = q/{displaymath}tsimeqt_0+(540-261.515)slash0.61652137simeqt_0+452,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1939.png"
 ALT="\begin{displaymath}
t\simeq t_0+(540-261.515)/0.61652137\simeq t_0 + 452 {\rm JD}.
\end{displaymath}">|; 

$key = q/+1^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$+1^\circ 26'$">|; 

$key = q/eleq0.21;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$e\leq 0.21$">|; 

$key = q/e';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1652.png"
 ALT="$e'$">|; 

$key = q/displaystylecosepsilon,{{bf{s}-sinepsilon,{{bf{q},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \cos\epsilon {\bf s} - \sin\epsilon {\bf q},$">|; 

$key = q/{{bf{e};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="${\bf e}$">|; 

$key = q/02^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="$02^\circ 34'$">|; 

$key = q/~-0^circ49';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$&nbsp;-0^\circ 49'$">|; 

$key = q/-1.680^circsimeq-1^circ41';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1322.png"
 ALT="$-1.680^\circ\simeq -1^\circ 41'$">|; 

$key = q/alpha_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\alpha_0$">|; 

$key = q/28.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1149.png"
 ALT="$28.8'$">|; 

$key = q/mu=0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1793.png"
 ALT="$\mu=0^\circ$">|; 

$key = q/29.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1167.png"
 ALT="$29.4'$">|; 

$key = q/90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$90^\circ$">|; 

$key = q/displaystylesin,delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle \sin \delta$">|; 

$key = q/-4.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1371.png"
 ALT="$-4.00$">|; 

$key = q/displaystylefrac{bar{z}-z}{deltaz},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1711.png"
 ALT="$\displaystyle \frac{\bar{z}-z}{\delta z},$">|; 

$key = q/10.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="$10.6'$">|; 

$key = q/+50^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="$+50^\circ 00'$">|; 

$key = q/{displaymath}beta_{Sa}=57.39'+deltabeta_1(M_M)-deltabeta_2(M_M)+deltabeta_3(M_S),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1597.png"
 ALT="\begin{displaymath}
\beta_{Sa} = 57.39' + \delta\beta_1(M_M)-\delta\beta_2 (M_M)+\delta\beta_3(M_S),
\end{displaymath}">|; 

$key = q/26.204;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1746.png"
 ALT="$26.204$">|; 

$key = q/{displaymath}cosA=-coslambda,sinL,sinalpha+sinlambda,cosL,sinepsilon+sinlambda,sinL,cosepsilon,cosalpha.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="519" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="\begin{displaymath}
\cos A= -\cos\lambda \sin L \sin\alpha +
\sin\lambda \...
...\sin \epsilon + \sin\lambda \sin L \cos\epsilon \cos\alpha.
\end{displaymath}">|; 

$key = q/30.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$30.4'$">|; 

$key = q/56.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1086.png"
 ALT="$56.6'$">|; 

$key = q/PiG'A;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1648.png"
 ALT="$\Pi G'A$">|; 

$key = q/13^circ25';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$13^\circ 25'$">|; 

$key = q/S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$S$">|; 

$key = q/bar{h};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2046.png"
 ALT="$\bar{h}$">|; 

$key = q/{displaymath}{{bf{r}=cosa,sinA,{{bf{e}+cosa,cosA,{{bf{n}+sina,{{bf{z}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="\begin{displaymath}
{\bf r} = \cos a \sin A {\bf e}+ \cos a \cos A {\bf n} + \sin a  {\bf z}
\end{displaymath}">|; 

$key = q/^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1192.png"
 ALT="$^m$">|; 

$key = q/33.482;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1841.png"
 ALT="$33.482$">|; 

$key = q/24';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="$24'$">|; 

$key = q/47.1^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1983.png"
 ALT="$47.1^\circ$">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.00118-0.9428)slash0.07059simeq0.83.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1857.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.00118-0.9428)/0.07059 \simeq 0.83.
\end{displaymath}">|; 

$key = q/74.813;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1820.png"
 ALT="$74.813$">|; 

$key = q/deltabeta_3=rho_{S,0},e_S,cosM_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1591.png"
 ALT="$\delta\beta_3=\rho_{S 0} e_S \cos M_S$">|; 

$key = q/{{bf{v};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="${\bf v}$">|; 

$key = q/+00^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="$+00^\circ 00'$">|; 

$key = q/displaystylecosepsilon,sinbeta+sinepsilon,cosbeta,sinlambda,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle \cos\epsilon \sin\beta +\sin\epsilon \cos\beta \sin\lambda,$">|; 

$key = q/46.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1953.png"
 ALT="$46.3^\circ$">|; 

$key = q/57.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1122.png"
 ALT="$57.8'$">|; 

$key = q/233^circ09'-18^circ07'=215^circ02';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$233^\circ 09'-18^\circ 07'=215^\circ 02'$">|; 

$key = q/+8^circ37';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$+8^\circ 37'$">|; 

$key = q/-321.453;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1766.png"
 ALT="$-321.453$">|; 

$key = q/Theta_-=0.107;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2129.png"
 ALT="$\Theta_-=0.107$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q+theta=297.661-7.345+42.453=332.769simeq332^circ46'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1762.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda} + q + \theta= 297.661-7.345+42.453=332.769 \simeq 332^\circ 46'.
\end{displaymath}">|; 

$key = q/180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$180^\circ$">|; 

$key = q/q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$q$">|; 

$key = q/0.5';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1722.png"
 ALT="$0.5'$">|; 

$key = q/{displaymath}deltah_-(208^circ)=0.014,mbox{hspace{0.5cm}}bar{h}(208^circ)=1.197,mbox{hspace{0.5cm}}deltah_+(208^circ)=0.016,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="463" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2079.png"
 ALT="\begin{displaymath}
\delta h_-(208^\circ) = 0.014,\mbox{\hspace{0.5cm}}\bar{h}(2...
...rc)=1.197, \mbox{\hspace{0.5cm}}\delta h_+(208^\circ) = 0.016,
\end{displaymath}">|; 

$key = q/beta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\beta$">|; 

$key = q/gamma;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$\gamma$">|; 

$key = q/+180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="$+180^\circ$">|; 

$key = q/50.3'';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2158.png"
 ALT="$50.3''$">|; 

$key = q/-50^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$-50^\circ$">|; 

$key = q/{displaymath}q(321^circ)=-7.345^circ,mbox{hspace{0.5cm}}zeta(321^circ)=6.912times10^{-2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1753.png"
 ALT="\begin{displaymath}
q(321^\circ)= -7.345^\circ,\mbox{\hspace{0.5cm}}\zeta(321^\circ)=6.912\times 10^{-2}.
\end{displaymath}">|; 

$key = q/180+2,sin^{-1}(tanL,tanepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$180 +2 \sin ^{-1}(\tan L \tan\epsilon)$">|; 

$key = q/52';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="$52'$">|; 

$key = q/280.458;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="$280.458$">|; 

$key = q/rslasha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="$r/a$">|; 

$key = q/D=0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1446.png"
 ALT="$D = 0^\circ$">|; 

$key = q/89.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="$89.9$">|; 

$key = q/+40^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$+40^\circ $">|; 

$key = q/{{bf{S};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1641.png"
 ALT="${\bf S}$">|; 

$key = q/14';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$14'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere5.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere5.eps}}
\end{figure}">|; 

$key = q/DeltaM_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1469.png"
 ALT="$\Delta M_M$">|; 

$key = q/a_2=2tilde{D}-M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1224.png"
 ALT="$a_2=2\tilde{D} - M$">|; 

$key = q/displaystylefrac{cosdelta,sin(alpha-alpha_0)}{cosL,sindelta-sinL,cosdelta,cos(alpha-alpha_0)}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle \frac{\cos \delta \sin (\alpha-\alpha_0)}{\cos L \sin \delta - \sin L \cos\delta \cos(\alpha - \alpha_0)}.$">|; 

$key = q/n(^circslash{{rm{day});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1417.png"
 ALT="$n(^\circ/{\rm day})$">|; 

$key = q/{displaymath}bar{lambda}=bar{lambda}_0+n,(t-t_0),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="\begin{displaymath}
\bar{\lambda} = \bar{\lambda}_0+ n (t -t_0),
\end{displaymath}">|; 

$key = q/displaystylebar{theta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1704.png"
 ALT="$\displaystyle \bar{\theta}$">|; 

$key = q/GM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1305.png"
 ALT="$GM$">|; 

$key = q/a';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1324.png"
 ALT="$a'$">|; 

$key = q/Omega;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1297.png"
 ALT="$\Omega$">|; 

$key = q/0.98564735;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="$0.98564735$">|; 

$key = q/26.415;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1240.png"
 ALT="$26.415$">|; 

$key = q/{displaymath}tanlambda=frac{cosL,sinalpha}{cosL,cosepsilon,cosalpha-sinepsilon,sinL}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="\begin{displaymath}
\tan \lambda = \frac{\cos L \sin \alpha}{\cos L \cos\epsilon \cos\alpha-\sin\epsilon \sin L}.
\end{displaymath}">|; 

$key = q/bar{lambda}_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="$\bar{\lambda}_0$">|; 

$key = q/{displaymath}q(294^circ)=-0.712^circ,mbox{hspace{0.5cm}}zeta(294^circ)=2.72times10^{-3},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1902.png"
 ALT="\begin{displaymath}
q(294^\circ)= -0.712^\circ, \mbox{\hspace{0.5cm}}\zeta(294^\circ)=2.72\times 10^{-3},
\end{displaymath}">|; 

$key = q/34.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1006.png"
 ALT="$34.0'$">|; 

$key = q/37.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1102.png"
 ALT="$37.2'$">|; 

$key = q/displaystyletheta(mu,bar{z})equivtan^{-1}left(frac{sinmu}{a^{-1},bar{z}+cosmu}right),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1881.png"
 ALT="$\displaystyle \theta(\mu,\bar{z})\equiv \tan^{-1} \left(\frac{\sin\mu}{a^{-1} \bar{z}+\cos\mu}\right),$">|; 

$key = q/Deltabar{F}=bar{F}-bar{F}_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1426.png"
 ALT="$\Delta\bar{F}= \bar{F}-\bar{F}_0$">|; 

$key = q/bar{z}=1.00109;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1832.png"
 ALT="$\bar{z}= 1.00109$">|; 

$key = q/theta(mu,z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1675.png"
 ALT="$\theta(\mu,z)$">|; 

$key = q/-265.928;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1534.png"
 ALT="$-265.928$">|; 

$key = q/bar{z}=(1+e,e_S)slash(1-e_S^{,2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1715.png"
 ALT="$\bar{z} = (1+e e_S)/(1-e_S^{ 2})$">|; 

$key = q/12';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="$12'$">|; 

$key = q/displaystylezeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1668.png"
 ALT="$\displaystyle \zeta$">|; 

$key = q/q_3(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1432.png"
 ALT="$q_3(^\circ)$">|; 

$key = q/z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1674.png"
 ALT="$z$">|; 

$key = q/132.334;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1956.png"
 ALT="$132.334$">|; 

$key = q/epsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\epsilon$">|; 

$key = q/+66^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="$+66^\circ 34'$">|; 

$key = q/-232.017;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="$-232.017$">|; 

$key = q/phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="$\phi$">|; 

$key = q/0.016711;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="$0.016711$">|; 

$key = q/s;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1194.png"
 ALT="$s$">|; 

$key = q/42';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="$42'$">|; 

$key = q/08.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1147.png"
 ALT="$08.8'$">|; 

$key = q/44.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1013.png"
 ALT="$44.2'$">|; 

$key = q/+3.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1402.png"
 ALT="$+3.00$">|; 

$key = q/deltaa_0=Rslasha_M=0.0166=56.98';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1331.png"
 ALT="$\delta a_0 = R/a_M = 0.0166=56.98'$">|; 

$key = q/330^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$330^\circ$">|; 

$key = q/-235.315;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="$-235.315$">|; 

$key = q/+43';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1379.png"
 ALT="$+43'$">|; 

$key = q/100^d06^h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="$100^d06^h$">|; 

$key = q/-1^circ41';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2068.png"
 ALT="$-1^\circ 41'$">|; 

$key = q/bar{F}_0=204.436^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1992.png"
 ALT="$\bar{F}_0 = 204.436^\circ$">|; 

$key = q/-328.142;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1767.png"
 ALT="$-328.142$">|; 

$key = q/PXY;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="$PXY$">|; 

$key = q/180-2,sin^{-1}(tanL,tanepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$180-2  \sin^{-1}(\tan L \tan\epsilon)$">|; 

$key = q/+60^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$+60^\circ $">|; 

$key = q/MM';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$MM'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashaltitude1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="337" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/altitude1.eps}}
\end{figure}">|; 

$key = q/displaystylexi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1710.png"
 ALT="$\displaystyle \xi$">|; 

$key = q/lambda=90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\lambda = 90^\circ$">|; 

$key = q/+2.7;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="$+2.7$">|; 

$key = q/{displaymath}M=M_0+tilde{n},(t-t_0),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="\begin{displaymath}
M = M_0 + \tilde{n} (t-t_0),
\end{displaymath}">|; 

$key = q/M_0=174.693^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1991.png"
 ALT="$M_0 = 174.693^\circ$">|; 

$key = q/+1^circ22';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$+1^\circ 22'$">|; 

$key = q/13.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img986.png"
 ALT="$13.4'$">|; 

$key = q/17.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1118.png"
 ALT="$17.8'$">|; 

$key = q/{displaymath}t=t_0+81-2.177slash0.98564735simeqt_0+78.8,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="\begin{displaymath}
t = t_0 + 81 -2.177/0.98564735 \simeq t_0 + 78.8 {\rm JD},
\end{displaymath}">|; 

$key = q/sigma;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$\sigma$">|; 

$key = q/321.491;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1750.png"
 ALT="$321.491$">|; 

$key = q/displaystylebar{F}+q_1+q_2+q_3+q_4+q_5,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1311.png"
 ALT="$\displaystyle \bar{F}+q_1+q_2+q_3+q_4+q_5,$">|; 

$key = q/41';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="$41'$">|; 

$key = q/(3slash2),e,a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="$(3/2) e a$">|; 

$key = q/lambda_S=44.602^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1232.png"
 ALT="$\lambda_S = 44.602^\circ$">|; 

$key = q/displaystyle1-e,cosM+e^2,sin^2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="$\displaystyle 1 -e \cos M + e^2 \sin^2 M,$">|; 

$key = q/rhoslasha=e,cosM+(1-e^2,sin^2M)^{1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="$\rho/a = e \cos M +(1-e^2 \sin^2 M)^{1/2}$">|; 

$key = q/zeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$\zeta$">|; 

$key = q/4.156;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1822.png"
 ALT="$4.156$">|; 

$key = q/06';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="$06'$">|; 

$key = q/21.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img915.png"
 ALT="$21.0'$">|; 

$key = q/57.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1104.png"
 ALT="$57.2'$">|; 

$key = q/-6^circ28';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="$-6^\circ 28'$">|; 

$key = q/F(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1441.png"
 ALT="$F (^\circ)$">|; 

$key = q/+8^circ30';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$+8^\circ 30'$">|; 

$key = q/Theta_-=-0.355;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2114.png"
 ALT="$\Theta_-=-0.355$">|; 

$key = q/01';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="$01'$">|; 

$key = q/14.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1022.png"
 ALT="$14.6'$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{128^circ45'{&{010^circ06'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="973" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $128^\circ 45'$&amp; $010^\circ 06'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/05';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="$05'$">|; 

$key = q/61^d06^h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="$61^d 06^h$">|; 

$key = q/{{bf{P'};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1875.png"
 ALT="${\bf P'}$">|; 

$key = q/0.05';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2042.png"
 ALT="$0.05'$">|; 

$key = q/a_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1550.png"
 ALT="$a_S$">|; 

$key = q/a-deltaa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1335.png"
 ALT="$a-\delta a$">|; 

$key = q/(1slash2),e^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="$(1/2) e^2$">|; 

$key = q/03.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img979.png"
 ALT="$03.2'$">|; 

$key = q/rslashr'=a,z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2020.png"
 ALT="$r/r' = a z$">|; 

$key = q/111.619;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1745.png"
 ALT="$111.619$">|; 

$key = q/59.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1170.png"
 ALT="$59.4'$">|; 

$key = q/26.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1083.png"
 ALT="$26.6'$">|; 

$key = q/252.087;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="$252.087$">|; 

$key = q/+1.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1395.png"
 ALT="$+1.00$">|; 

$key = q/|tanL,tandelta|<1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$\vert\tan L \tan\delta\vert&lt;1$">|; 

$key = q/+80^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="$+80^\circ 00'$">|; 

$key = q/360^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$360^\circ$">|; 

$key = q/varpi';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1653.png"
 ALT="$\varpi'$">|; 

$key = q/+9^circ58';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="$+9^\circ 58'$">|; 

$key = q/132.342;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2131.png"
 ALT="$132.342$">|; 

$key = q/10^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$10^\circ$">|; 

$key = q/a_5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1229.png"
 ALT="$a_5$">|; 

$key = q/19.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1160.png"
 ALT="$19.2'$">|; 

$key = q/21';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="$21'$">|; 

$key = q/17';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="$17'$">|; 

$key = q/09.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1171.png"
 ALT="$09.6'$">|; 

$key = q/19.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1154.png"
 ALT="$19.0'$">|; 

$key = q/d;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="$d$">|; 

$key = q/rho_M>rho_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1582.png"
 ALT="$\rho_M&gt;\rho_S$">|; 

$key = q/5.197;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1287.png"
 ALT="$5.197$">|; 

$key = q/179.096;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1508.png"
 ALT="$179.096$">|; 

$key = q/MGM';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1304.png"
 ALT="$MGM'$">|; 

$key = q/{displaymath}q(181^circ)=-0.091^circ,mbox{hspace{0.5cm}}zeta(181^circ)=-4.838times10^{-2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1828.png"
 ALT="\begin{displaymath}
q(181^\circ)= -0.091^\circ,\mbox{\hspace{0.5cm}}\zeta(181^\circ)=-4.838\times 10^{-2}.
\end{displaymath}">|; 

$key = q/+16^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="$+16^\circ 34'$">|; 

$key = q/04.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1027.png"
 ALT="$04.8'$">|; 

$key = q/a=36^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$a=36^\circ 26'$">|; 

$key = q/-47.162;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1772.png"
 ALT="$-47.162$">|; 

$key = q/09^circ46';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$09^\circ 46'$">|; 

$key = q/0^circleqmuleq180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$0^\circ\leq \mu\leq 180^\circ$">|; 

$key = q/53.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1002.png"
 ALT="$53.8'$">|; 

$key = q/1077.813;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1501.png"
 ALT="$1077.813$">|; 

$key = q/displaystyler;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="$\displaystyle r$">|; 

$key = q/0.7';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$0.7'$">|; 

$key = q/|beta_{syz}|<beta_{M};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1592.png"
 ALT="$\vert\beta_{syz}\vert&lt; \beta_{M}$">|; 

$key = q/M_S(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1481.png"
 ALT="$M_S(^\circ)$">|; 

$key = q/06^circ23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="$06^\circ 23'$">|; 

$key = q/PQPi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="$PQ\Pi$">|; 

$key = q/{figure}{epsfysize{=3.in{centerline{epsffile{epsfilesslashfig1.2x.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="337" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="\begin{figure}
\epsfysize =3.in
\centerline{\epsffile{epsfiles/fig1.2x.eps}}
\end{figure}">|; 

$key = q/42.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img953.png"
 ALT="$42.2'$">|; 

$key = q/8.870;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1494.png"
 ALT="$8.870$">|; 

$key = q/04.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1015.png"
 ALT="$04.4'$">|; 

$key = q/deltaz=0.02349;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1907.png"
 ALT="$\delta z = 0.02349$">|; 

$key = q/-659.536;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1774.png"
 ALT="$-659.536$">|; 

$key = q/13.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img980.png"
 ALT="$13.2'$">|; 

$key = q/39.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1180.png"
 ALT="$39.8'$">|; 

$key = q/20.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="$20.2'$">|; 

$key = q/126^circ32';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$126^\circ 32'$">|; 

$key = q/218.322;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1247.png"
 ALT="$218.322$">|; 

$key = q/SP^2=SL^2+PL^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="$SP^2 = SL^2+ PL^2$">|; 

$key = q/0.52404094;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2150.png"
 ALT="$0.52404094$">|; 

$key = q/{displaymath}q_1(a_1)=5.555^circ,~~q_2(a_2)=-0.663^circ,~~q_3(a_3)=-0.631^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1260.png"
 ALT="\begin{displaymath}
q_1(a_1)=5.555^\circ,&nbsp;&nbsp;q_2(a_2)= -0.663^\circ,&nbsp;&nbsp;q_3(a_3) = -0.631^\circ,
\end{displaymath}">|; 

$key = q/beta(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1442.png"
 ALT="$\beta(^\circ)$">|; 

$key = q/beta_{syz}=4.790^circsimeq4^circ47';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1575.png"
 ALT="$\beta_{syz} = 4.790^\circ\simeq 4^\circ 47'$">|; 

$key = q/-06';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1397.png"
 ALT="$-06'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashlong1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img2105.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/long1.eps}}
\end{figure}">|; 

$key = q/alpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\alpha$">|; 

$key = q/01.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="$01.0'$">|; 

$key = q/displaystyledeltatheta_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1707.png"
 ALT="$\displaystyle \delta\theta_+$">|; 

$key = q/F;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1298.png"
 ALT="$F$">|; 

$key = q/-191.810;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1913.png"
 ALT="$-191.810$">|; 

$key = q/alpharightarrowalpha+180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\alpha \rightarrow \alpha+180^\circ$">|; 

$key = q/{displaymath}q=2,e,sinM+(5slash4),e^2,sin,2M,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="\begin{displaymath}
q = 2 e \sin M + (5/4) e^2 \sin 2M,
\end{displaymath}">|; 

$key = q/45.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1049.png"
 ALT="$45.4'$">|; 

$key = q/e_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1461.png"
 ALT="$e_M$">|; 

$key = q/displaystylesina;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle \sin a$">|; 

$key = q/q=-16.974^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2127.png"
 ALT="$q= -16.974^\circ$">|; 

$key = q/14^h20^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$14^h 20^m$">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.00184-0.9230)slash0.11014simeq0.72.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1759.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.00184-0.9230)/0.11014 \simeq 0.72.
\end{displaymath}">|; 

$key = q/13^circ38';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="$13^\circ 38'$">|; 

$key = q/14.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1010.png"
 ALT="$14.2'$">|; 

$key = q/187^circ30';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1368.png"
 ALT="$187^\circ 30'$">|; 

$key = q/bar{lambda}_0=50.059^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1872.png"
 ALT="$\bar{\lambda}_0 = 50.059^\circ$">|; 

$key = q/030^circ47';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1414.png"
 ALT="$030^\circ 47'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashparallax.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="507" HEIGHT="341" BORDER="0"
 SRC="|."$dir".q|img1323.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/parallax.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{r}{a}=[1-2,e,cosM,(1-e^2,sin^2M)^{1slash2}+e^2+2,e^2,sin^2M]^{1slash2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="451" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="\begin{displaymath}
\frac{r}{a} = [1-2 e \cos M (1-e^2 \sin^2 M)^{1/2}+e^2+2 e^2 \sin^2 M]^{1/2}.
\end{displaymath}">|; 

$key = q/46.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1091.png"
 ALT="$46.8'$">|; 

$key = q/4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$4'$">|; 

$key = q/epsilon=23^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\epsilon = 23^\circ 26'$">|; 

$key = q/26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="$26'$">|; 

$key = q/bar{lambda}_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1460.png"
 ALT="$\bar{\lambda}_S$">|; 

$key = q/-49';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1415.png"
 ALT="$-49'$">|; 

$key = q/sina_{{rm{+}=cos(L-delta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\sin a_{\rm +} = \cos (L-\delta)$">|; 

$key = q/0.053862;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="$0.053862$">|; 

$key = q/displaystyleleft(frac{{{bf{r}cdot{{bf{e}}{{{bf{r}cdot{{bf{n}}right),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle \left(\frac{{\bf r}\cdot {\bf e}}{{\bf r}\cdot {\bf n}}\right),$">|; 

$key = q/34.365;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="$34.365$">|; 

$key = q/Deltabar{lambda}=bar{lambda}-bar{lambda}_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1185.png"
 ALT="$\Delta\bar{\lambda} = \bar{\lambda}-\bar{\lambda}_0$">|; 

$key = q/+60^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="$+60^\circ 00'$">|; 

$key = q/SR=CR-CS;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="$SR = CR-CS$">|; 

$key = q/301.468;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1243.png"
 ALT="$301.468$">|; 

$key = q/arightarrowa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$a\rightarrow a$">|; 

$key = q/PiSCQA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="$\Pi S C Q A$">|; 

$key = q/v=r,sini,sinF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2011.png"
 ALT="$v= r \sin i \sin F$">|; 

$key = q/alpha_0=180^circ+alpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\alpha_0=180^\circ + \alpha$">|; 

$key = q/075^circ13';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1396.png"
 ALT="$075^\circ 13'$">|; 

$key = q/-6.532;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1280.png"
 ALT="$-6.532$">|; 

$key = q/{{bf{p};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="${\bf p}$">|; 

$key = q/1.781;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2091.png"
 ALT="$1.781$">|; 

$key = q/bar{lambda}_0=181.973^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1980.png"
 ALT="$\bar{\lambda}_0 = 181.973^\circ$">|; 

$key = q/6.6%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1613.png"
 ALT="$6.6\%$">|; 

$key = q/displaystyle[2,e-(1slash4),e^3],sin,M+(5slash4),e^2,sin,2M+(13slash12),e^3,sin,3M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="464" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1887.png"
 ALT="$\displaystyle [2 e - (1/4) e^3] \sin  M + (5/4)  e^2 sin 2M + (13/12) e^3 \sin  3M,$">|; 

$key = q/-354.803;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1284.png"
 ALT="$-354.803$">|; 

$key = q/{displaymath}q_1(a_1)=5.562^circ,~~q_2(a_2)=1.311^circ,~~q_3(a_3)=-0.394^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1292.png"
 ALT="\begin{displaymath}
q_1(a_1)=5.562^\circ,&nbsp;&nbsp;q_2(a_2)= 1.311^\circ,&nbsp;&nbsp;q_3(a_3) = -0.394^\circ,
\end{displaymath}">|; 

$key = q/n-tilde{n}=0.11140,^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1217.png"
 ALT="$n-\tilde{n} = 0.11140  ^\circ $">|; 

$key = q/VUV'U';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$VUV'U'$">|; 

$key = q/4.2%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1611.png"
 ALT="$4.2\%$">|; 

$key = q/+1.1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$+1.1$">|; 

$key = q/displaystylecosT;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="$\displaystyle \cos T$">|; 

$key = q/196.7^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1815.png"
 ALT="$196.7^\circ$">|; 

$key = q/273.259;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="$273.259$">|; 

$key = q/mu=360^circ-162^circ11'=197^circ49';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$\mu=360^\circ -162^\circ 11'=197^\circ 49'$">|; 

$key = q/49.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1181.png"
 ALT="$49.8'$">|; 

$key = q/21.0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2006.png"
 ALT="$21.0^\circ$">|; 

$key = q/(180-163.3)slash0.46157617simeq36;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1816.png"
 ALT="$(180-163.3)/0.46157617\simeq 36$">|; 

$key = q/9.536651;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="$9.536651$">|; 

$key = q/delta=90^circ-L;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$\delta = 90^\circ - L$">|; 

$key = q/musimeq287^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2094.png"
 ALT="$\mu\simeq 287^\circ$">|; 

$key = q/lambda_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1444.png"
 ALT="$\lambda_M$">|; 

$key = q/16';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="$16'$">|; 

$key = q/59';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="$59'$">|; 

$key = q/displaystylelambda;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="$\displaystyle \lambda$">|; 

$key = q/dlambdaslashdt=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1812.png"
 ALT="$d\lambda/dt = 0$">|; 

$key = q/q(M);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="$q(M)$">|; 

$key = q/DeltaM_M=M_M-M_{M,0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1627.png"
 ALT="$\Delta M_M= M_M-M_{M 0}$">|; 

$key = q/18.0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2009.png"
 ALT="$18.0^\circ$">|; 

$key = q/displaystyledeltatheta_+(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1691.png"
 ALT="$\displaystyle \delta\theta_+(\mu)$">|; 

$key = q/displaystyle{{bf{q};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle {\bf q}$">|; 

$key = q/130^d02^h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="$130^d02^h$">|; 

$key = q/23.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img999.png"
 ALT="$23.8'$">|; 

$key = q/displaystyle{{bf{r}cdot{{bf{q},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle {\bf r}\cdot {\bf q},$">|; 

$key = q/{displaymath}Theta_-(0.69)=0.107,mbox{hspace{0.5cm}}Theta_+(0.69)=0.583,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1974.png"
 ALT="\begin{displaymath}
\Theta_-(0.69) = 0.107, \mbox{\hspace{0.5cm}}\Theta_+(0.69) = 0.583,
\end{displaymath}">|; 

$key = q/{displaymath}t=t_0+171.6,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="\begin{displaymath}
t = t_0+ 171.6  {\rm JD},
\end{displaymath}">|; 

$key = q/36';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="$36'$">|; 

$key = q/18.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1142.png"
 ALT="$18.6'$">|; 

$key = q/183^circ07';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1373.png"
 ALT="$183^\circ 07'$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{epsfilesslashsolstice.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="401" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{epsfiles/solstice.eps}}
\end{figure}">|; 

$key = q/~+6^circ41';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="$&nbsp;+6^\circ 41'$">|; 

$key = q/0.08308122;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2152.png"
 ALT="$0.08308122$">|; 

$key = q/bar{F};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1212.png"
 ALT="$\bar{F}$">|; 

$key = q/SCQequivE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$SCQ\equiv E$">|; 

$key = q/DeltaM(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1184.png"
 ALT="$\Delta M(^\circ)$">|; 

$key = q/0.048386;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="$0.048386$">|; 

$key = q/displaystylebar{lambda}+q+theta.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1714.png"
 ALT="$\displaystyle \bar{\lambda} + q+ \theta.$">|; 

$key = q/VR'V';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$VR'V'$">|; 

$key = q/bar{lambda}_0=355.460^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1864.png"
 ALT="$\bar{\lambda}_0 = 355.460^\circ$">|; 

$key = q/{displaymath}F=bar{F}+q=1.781+2.561=4.342simeq4^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2092.png"
 ALT="\begin{displaymath}
F = \bar{F} + q =1.781+2.561 = 4.342\simeq 4^\circ.
\end{displaymath}">|; 

$key = q/132.377;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1955.png"
 ALT="$132.377$">|; 

$key = q/{displaymath}deltaasimeqdeltaa_0,cosa,(1+e,cosM),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1330.png"
 ALT="\begin{displaymath}
\delta a \simeq \delta a_0 \cos a (1+e \cos M),
\end{displaymath}">|; 

$key = q/-64.495;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1519.png"
 ALT="$-64.495$">|; 

$key = q/-40';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1408.png"
 ALT="$-40'$">|; 

$key = q/CS;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$CS$">|; 

$key = q/0.493;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="$0.493$">|; 

$key = q/48.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1127.png"
 ALT="$48.0'$">|; 

$key = q/+0.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1391.png"
 ALT="$+0.00$">|; 

$key = q/M_Ssimeq65^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1568.png"
 ALT="$M_S\simeq 65^\circ$">|; 

$key = q/t=+1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1359.png"
 ALT="$t=+1$">|; 

$key = q/07^circ39';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$07^\circ 39'$">|; 

$key = q/80.107;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1896.png"
 ALT="$80.107$">|; 

$key = q/displaystyle1-e,cosM+(3slash2),e^2,sin^2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="$\displaystyle 1 -e \cos M + (3/2) e^2 \sin^2 M,$">|; 

$key = q/+90^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="$+90^\circ 00 '$">|; 

$key = q/R_SggR_E;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1562.png"
 ALT="$R_S\gg R_E$">|; 

$key = q/zeta_S=-8.56times10^{-3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1817.png"
 ALT="$\zeta_S= -8.56\times 10^{-3}$">|; 

$key = q/displaystyledeltaz=frac{e+e'}{1-e'^{,2}}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1679.png"
 ALT="$\displaystyle \delta z = \frac{e+e'}{1-e'^{ 2}}.$">|; 

$key = q/-2^circ08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$-2^\circ 08'$">|; 

$key = q/{displaymath}rho_Msimeqrho_{M,0},(1+e_M,cosM_M),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1553.png"
 ALT="\begin{displaymath}
\rho_M\simeq \rho_{M 0} (1+e_M \cos M_M),
\end{displaymath}">|; 

$key = q/-231.388;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="$-231.388$">|; 

$key = q/beta_{syz};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1564.png"
 ALT="$\beta_{syz}$">|; 

$key = q/displaystyleD;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1457.png"
 ALT="$\displaystyle D$">|; 

$key = q/+73^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="$+73^\circ 26'$">|; 

$key = q/+28^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="$+28^\circ 26'$">|; 

$key = q/0.08312507;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$0.08312507$">|; 

$key = q/displaystylecosL,cosalpha_0,{{bf{v}+cosL,sinalpha_0,{{bf{u}+sinL,{{bf{p}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle \cos L \cos \alpha_0 {\bf v} + \cos L \sin \alpha_0 {\bf u} + \sin L {\bf p}.$">|; 

$key = q/03^circ58';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$03^\circ 58'$">|; 

$key = q/{displaymath}h=Theta_-,deltah_-+bar{h}+Theta_+,deltah_+=-0.469times0.014+1.197-0.121times0.016=1.188.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2080.png"
 ALT="\begin{displaymath}
h = \Theta_- \delta h_- + \bar{h}+\Theta_+ \delta h_+ = -0.469\times 0.014 +1.197-0.121\times 0.016 = 1.188.
\end{displaymath}">|; 

$key = q/displaystylelambda_S+theta.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1883.png"
 ALT="$\displaystyle \lambda_S+ \theta.$">|; 

$key = q/beta_{St}(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1605.png"
 ALT="$\beta_{St}(')$">|; 

$key = q/R_U=R_E-x=R_E-r_M,rho_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1560.png"
 ALT="$R_U = R_E-x=
R_E - r_M \rho_S$">|; 

$key = q/09^circ06';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$09^\circ 06'$">|; 

$key = q/|beta_{syz}|<beta_{S};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1600.png"
 ALT="$\vert\beta_{syz}\vert&lt; \beta_{S}$">|; 

$key = q/110^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1393.png"
 ALT="$110^\circ 34'$">|; 

$key = q/19';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="$19'$">|; 

$key = q/^ast48;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="$^\ast 48$">|; 

$key = q/displaystylecoslambda,(cosL,cosepsilon+sinL,sinepsilon,sinalpha_0).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$\displaystyle \cos\lambda (\cos L \cos\epsilon + \sin L \sin\epsilon \sin\alpha_0).$">|; 

$key = q/16.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1064.png"
 ALT="$16.0'$">|; 

$key = q/27.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1095.png"
 ALT="$27.0'$">|; 

$key = q/{displaymath}cosT=frac{cosE-e}{1-e,cosE}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="\begin{displaymath}
\cos T = \frac{\cos E - e}{1-e \cos E}.
\end{displaymath}">|; 

$key = q/Q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$Q$">|; 

$key = q/PCPi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="$PC\Pi$">|; 

$key = q/tanA=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\tan A = 0$">|; 

$key = q/2.14;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1805.png"
 ALT="$2.14$">|; 

$key = q/dbar{theta}slashdbar{mu}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1948.png"
 ALT="$d\bar{\theta}/d\bar{\mu}=0$">|; 

$key = q/|beta_{syz}|;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1602.png"
 ALT="$\vert\beta_{syz}\vert$">|; 

$key = q/q_5(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1434.png"
 ALT="$q_5(^\circ)$">|; 

$key = q/delta=41.050';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1340.png"
 ALT="$\delta = 41.050'$">|; 

$key = q/r'equivG'P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1665.png"
 ALT="$r'\equiv G'P$">|; 

$key = q/alpha_0=alpha-t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$\alpha_0=\alpha-t$">|; 

$key = q/{{bf{z}cdot{{bf{q}>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="${\bf z}\cdot{\bf q} &gt; 0$">|; 

$key = q/GL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1306.png"
 ALT="$GL$">|; 

$key = q/216.396;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1235.png"
 ALT="$216.396$">|; 

$key = q/{displaymath}{{rm{Area},PiRP=frac{b}{a},{{rm{Area},PiRQ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="\begin{displaymath}
{\rm Area} \Pi RP = \frac{b}{a} {\rm Area} \Pi RQ,
\end{displaymath}">|; 

$key = q/{displaymath}lambdasimeqbar{lambda}+bar{theta},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1806.png"
 ALT="\begin{displaymath}
\lambda \simeq \bar{\lambda} + \bar{\theta},
\end{displaymath}">|; 

$key = q/765.218;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1502.png"
 ALT="$765.218$">|; 

$key = q/{displaymath}tanalpha=cosepsilon,tan(bar{lambda}+q),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="\begin{displaymath}
\tan\alpha = \cos\epsilon \tan(\bar{\lambda}+q),
\end{displaymath}">|; 

$key = q/+3.7;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="$+3.7$">|; 

$key = q/displaystylecosbeta,coslambda,{{bf{v}+cosbeta,sinlambda,{{bf{s}+sinbeta,{{bf{q},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$\displaystyle \cos\beta \cos\lambda {\bf v} + \cos\beta \sin\lambda {\bf s} +\sin\beta {\bf q},$">|; 

$key = q/QP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="$QP$">|; 

$key = q/08.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1129.png"
 ALT="$08.2'$">|; 

$key = q/15.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1052.png"
 ALT="$15.6'$">|; 

$key = q/58.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1134.png"
 ALT="$58.2'$">|; 

$key = q/displaystylesinL,sindelta+cosL,cosdelta,cos(alpha-alpha_0),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle \sin L \sin \delta + \cos L \cos \delta \cos(\alpha-\alpha_0),$">|; 

$key = q/bar{lambda}_0=34.365^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1869.png"
 ALT="$\bar{\lambda}_0 = 34.365^\circ$">|; 

$key = q/lambda;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\lambda$">|; 

$key = q/a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$a$">|; 

$key = q/{displaymath}beta=h,beta_0=-0.587times0.423=-0.248simeq-0^circ15'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2125.png"
 ALT="\begin{displaymath}
\beta = h \beta_0 =- 0.587\times 0.423 = -0.248\simeq -0^\circ 15'.
\end{displaymath}">|; 

$key = q/displaystyleh,beta_0.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2039.png"
 ALT="$\displaystyle h \beta_0.$">|; 

$key = q/Msimeq294^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1901.png"
 ALT="$M\simeq 294^\circ$">|; 

$key = q/0.205636;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="$0.205636$">|; 

$key = q/38.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1126.png"
 ALT="$38.0'$">|; 

$key = q/74.773;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1821.png"
 ALT="$74.773$">|; 

$key = q/{displaymath}musimeqbar{mu}=bar{lambda}_S-bar{lambda}=bar{lambda}_{0,S}-bar{lamba}_0+(n_S-n),(t-t_0)=284.998+0.46157617,(t-t_0).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1790.png"
 ALT="\begin{displaymath}
\mu \simeq \bar{\mu} = \bar{\lambda}_S-\bar{\lambda} = \bar{...
...{\lambda}_0 +(n_S-n) (t-t_0) = 284.998 + 0.46157617 (t-t_0).
\end{displaymath}">|; 

$key = q/+75^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="$+75^\circ 00'$">|; 

$key = q/N';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1296.png"
 ALT="$N'$">|; 

$key = q/-17.610;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1275.png"
 ALT="$-17.610$">|; 

$key = q/245.5^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1862.png"
 ALT="$245.5^\circ$">|; 

$key = q/deltaz=0.11014;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1758.png"
 ALT="$\delta z = 0.11014$">|; 

$key = q/dag;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="$\dag$">|; 

$key = q/12.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img968.png"
 ALT="$12.8'$">|; 

$key = q/53.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img996.png"
 ALT="$53.6'$">|; 

$key = q/bar{z}=(1+e,e_S)slash(1-e^{2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2109.png"
 ALT="$\bar{z} = (1+e e_S)/(1-e^{2})$">|; 

$key = q/-231.360;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="$-231.360$">|; 

$key = q/displaystylebar{theta}(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1687.png"
 ALT="$\displaystyle \bar{\theta}(\mu)$">|; 

$key = q/{displaymath}a_3=tilde{D}simeq106^circ,~~~a_4=M_Ssimeq354^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1290.png"
 ALT="\begin{displaymath}
a_3=\tilde{D}\simeq 106^\circ,&nbsp;&nbsp;&nbsp;a_4 = M_S\simeq 354^\circ,
\end{displaymath}">|; 

$key = q/29.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1155.png"
 ALT="$29.0'$">|; 

$key = q/musimeq114^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2064.png"
 ALT="$\mu\simeq 114^\circ$">|; 

$key = q/0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$0^\circ $">|; 

$key = q/21^circ27';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="$21^\circ 27'$">|; 

$key = q/G;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$G$">|; 

$key = q/q_2=-0.663^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1317.png"
 ALT="$q_2=-0.663^\circ$">|; 

$key = q/30.157;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1842.png"
 ALT="$30.157$">|; 

$key = q/07.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1105.png"
 ALT="$07.4'$">|; 

$key = q/{displaymath}q(88^circ)=10.739^circ,mbox{hspace{0.5cm}}zeta(88^circ)=-5.45times10^{-3},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1779.png"
 ALT="\begin{displaymath}
q(88^\circ)= 10.739^\circ, \mbox{\hspace{0.5cm}}\zeta(88^\circ)=-5.45\times 10^{-3},
\end{displaymath}">|; 

$key = q/beta_0(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2155.png"
 ALT="$\beta_0(^\circ)$">|; 

$key = q/breve{n}-n=5.2954times10^{-2},^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1303.png"
 ALT="$\breve{n}-n = 5.2954\times 10^{-2}  ^\circ$">|; 

$key = q/{displaymath}a_5=2bar{F}=2times5.197=10.394simeq10^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1291.png"
 ALT="\begin{displaymath}
a_5=2\bar{F} = 2\times 5.197=10.394\simeq 10^\circ.
\end{displaymath}">|; 

$key = q/40^circ23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1377.png"
 ALT="$40^\circ 23'$">|; 

$key = q/58.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1152.png"
 ALT="$58.8'$">|; 

$key = q/T=M+q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="$T = M + q$">|; 

$key = q/25.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1041.png"
 ALT="$25.2'$">|; 

$key = q/{displaymath}Theta_-(-0.48)=-0.355,mbox{hspace{0.5cm}}Theta_+(-0.48)=-0.125,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1909.png"
 ALT="\begin{displaymath}
\Theta_-(-0.48) = -0.355, \mbox{\hspace{0.5cm}}\Theta_+(-0.48) = -0.125,
\end{displaymath}">|; 

$key = q/6.615;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1246.png"
 ALT="$6.615$">|; 

$key = q/displaystylea,(1-e,cosE),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$\displaystyle a (1- e \cos E),$">|; 

$key = q/z_{{rm{min};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1697.png"
 ALT="$z_{\rm min}$">|; 

$key = q/q(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1189.png"
 ALT="$q(^\circ)$">|; 

$key = q/KS=(3slash2),e,a,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$KS=(3/2) e a \cos M$">|; 

$key = q/beta_{St},beta_{Sa}<|beta_{syz}|<beta_{S};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1603.png"
 ALT="$\beta_{St},\beta_{Sa}&lt;\vert\beta_{syz}\vert&lt; \beta_{S}$">|; 

$key = q/11.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img938.png"
 ALT="$11.8'$">|; 

$key = q/180.244^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1802.png"
 ALT="$180.244^\circ$">|; 

$key = q/rho_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2160.png"
 ALT="$\rho_S$">|; 

$key = q/455.710;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2074.png"
 ALT="$455.710$">|; 

$key = q/+06^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="$+06^\circ 34'$">|; 

$key = q/{{bf{z}cdot{{bf{q}rightarrow-{{bf{z}cdot{{bf{q};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="${\bf z}\cdot{\bf q} \rightarrow -{\bf z}\cdot{\bf q}$">|; 

$key = q/{displaymath}a_3=tilde{D}simeq314^circ,~~~a_4=M_Ssimeq120^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1258.png"
 ALT="\begin{displaymath}
a_3=\tilde{D}\simeq 314^\circ,&nbsp;&nbsp;&nbsp;a_4 = M_S\simeq 120^\circ,
\end{displaymath}">|; 

$key = q/17.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1106.png"
 ALT="$17.4'$">|; 

$key = q/delta=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\delta=0$">|; 

$key = q/a,(AU);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="$a (AU)$">|; 

$key = q/displaystyle2,e,sin,M+(5slash4),e^2,sin,2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1700.png"
 ALT="$\displaystyle 2 e \sin  M + (5/4) e^2 \sin 2M,$">|; 

$key = q/-134.519;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1269.png"
 ALT="$-134.519$">|; 

$key = q/+1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1684.png"
 ALT="$+1$">|; 

$key = q/42.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img947.png"
 ALT="$42.0'$">|; 

$key = q/ZP=(1slash2),e,a,sinM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$ZP=(1/2) e a \sin M$">|; 

$key = q/47';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="$47'$">|; 

$key = q/27';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="$27'$">|; 

$key = q/{displaymath}h(mu,z)=left[1+2,(a,z)^{-1},cosmu+(a,z)^{-2}right]^{-1slash2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img2023.png"
 ALT="\begin{displaymath}
h(\mu,z) = \left[1 + 2 (a z)^{-1} \cos\mu+ (a z)^{-2}\right]^{-1/2}
\end{displaymath}">|; 

$key = q/18.5^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2004.png"
 ALT="$18.5^\circ$">|; 

$key = q/{displaymath}sinq=frac{PL}{SP}=frac{2,e,sinM}{[1-2,e,cosM,(1-e^2,sin^2M)^{1slash2}+e^2+2,e^2,sin^2M]^{1slash2}}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="529" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="\begin{displaymath}
\sin q = \frac{PL}{SP} = \frac{2 e \sin M}{[1-2 e \cos M (1-e^2 \sin^2 M)^{1/2}+e^2+2 e^2 \sin^2 M]^{1/2}}.
\end{displaymath}">|; 

$key = q/24.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1029.png"
 ALT="$24.8'$">|; 

$key = q/deltah_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2045.png"
 ALT="$\delta h_-$">|; 

$key = q/{{bf{n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="${\bf n}$">|; 

$key = q/51';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img468.png"
 ALT="$51'$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{epsfilesslashfigv5.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="582" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img1655.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{epsfiles/figv5.eps}}
\end{figure}">|; 

$key = q/06^circ43';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$06^\circ 43'$">|; 

$key = q/13^h13^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="$13^h13^m$">|; 

$key = q/{displaymath}|beta_{syz}|<delta_M+rho_M-rho_S.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1580.png"
 ALT="\begin{displaymath}
\vert\beta_{syz}\vert &lt; \delta_M+\rho_M-\rho_S.
\end{displaymath}">|; 

$key = q/+2.8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="$+2.8$">|; 

$key = q/-345.838;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1273.png"
 ALT="$-345.838$">|; 

$key = q/+46^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="$+46^\circ 34'$">|; 

$key = q/CB;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="$CB$">|; 

$key = q/+55^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$+55^\circ $">|; 

$key = q/displaystylesinlambda,sinepsilon,cosalpha_0,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$\displaystyle \sin\lambda \sin \epsilon \cos\alpha_0,$">|; 

$key = q/05.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1033.png"
 ALT="$05.0'$">|; 

$key = q/displaystyle-sinL,(cosL,cosepsilon+sinL,sinepsilon,sinalpha_0),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$\displaystyle -\sin L (\cos L \cos\epsilon + \sin L \sin \epsilon \sin \alpha_0),$">|; 

$key = q/210^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$210^\circ$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{epsfilesslashtotalm.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="612" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img1576.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{epsfiles/totalm.eps}}
\end{figure}">|; 

$key = q/displaystyletheta(mu,z_{{rm{min})-theta(mu,bar{z}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1692.png"
 ALT="$\displaystyle \theta(\mu,z_{\rm min}) - \theta(\mu,\bar{z}),$">|; 

$key = q/{displaymath}{{bf{r}=coslambda,{{bf{v}+sinlambda,{{bf{s}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="\begin{displaymath}
{\bf r} = \cos\lambda {\bf v} + \sin \lambda {\bf s}
\end{displaymath}">|; 

$key = q/14AQ00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$14AQ00$">|; 

$key = q/57.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1110.png"
 ALT="$57.4'$">|; 

$key = q/360^circ-alpha_c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$360^\circ - \alpha_c$">|; 

$key = q/Theta_+=0.583;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2130.png"
 ALT="$\Theta_+ = 0.583$">|; 

$key = q/deltah_pm(360^circ-mu)=deltah_pm(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2049.png"
 ALT="$\delta h_\pm(360^\circ - \mu) = \delta h_\pm(\mu)$">|; 

$key = q/+0^circ28';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="$+0^\circ 28'$">|; 

$key = q/31.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img928.png"
 ALT="$31.4'$">|; 

$key = q/trightarrowt;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$t\rightarrow t$">|; 

$key = q/P';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$P'$">|; 

$key = q/19.348;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="$19.348$">|; 

$key = q/PQKL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="$PQKL$">|; 

$key = q/displaystyleM+2,e,sinM+(5slash4),e^2,sin2M.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="$\displaystyle M + 2 e \sin M + (5/4) e^2 \sin 2M.$">|; 

$key = q/37.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1120.png"
 ALT="$37.8'$">|; 

$key = q/Theta_pm;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1719.png"
 ALT="$\Theta_\pm$">|; 

$key = q/deltabeta_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1638.png"
 ALT="$\delta\beta_2$">|; 

$key = q/{displaymath}r=a,(1-e,cosE),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="\begin{displaymath}
r = a (1-e \cos E),
\end{displaymath}">|; 

$key = q/displaystylesinepsilon,{{bf{s}+cosepsilon,{{bf{q}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle \sin\epsilon {\bf s} + \cos\epsilon {\bf q}.$">|; 

$key = q/1.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2111.png"
 ALT="$1.8'$">|; 

$key = q/1.917;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1894.png"
 ALT="$1.917$">|; 

$key = q/{displaymath}beta=h,beta_0=0.964times0.173=0.167simeq0^circ10'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2097.png"
 ALT="\begin{displaymath}
\beta = h \beta_0 = 0.964\times 0.173 = 0.167 \simeq 0^\circ 10'.
\end{displaymath}">|; 

$key = q/q_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1440.png"
 ALT="$q_4$">|; 

$key = q/45.218;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1506.png"
 ALT="$45.218$">|; 

$key = q/50.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="$50.6'$">|; 

$key = q/+3.4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$+3.4$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere8.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="337" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere8.eps}}
\end{figure}">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.00016-0.97909)slash0.02349simeq0.90.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1931.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.00016-0.97909)/0.02349 \simeq 0.90.
\end{displaymath}">|; 

$key = q/{displaymath}deltah_-(287^circ)=-0.002,mbox{hspace{0.5cm}}bar{h}(287^circ)=0.966,mbox{hspace{0.5cm}}deltah_+(287^circ)=-0.003,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2095.png"
 ALT="\begin{displaymath}
\delta h_-(287^\circ) = -0.002,\mbox{\hspace{0.5cm}}\bar{h}(...
...c)=0.966, \mbox{\hspace{0.5cm}}\delta h_+(287^\circ) = -0.003,
\end{displaymath}">|; 

$key = q/{displaymath}frac{y}{y'}=frac{b}{a},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="\begin{displaymath}
\frac{y}{y'} = \frac{b}{a},
\end{displaymath}">|; 

$key = q/+51^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="$+51^\circ 34'$">|; 

$key = q/displaystyle-deltaa,sinmu.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1356.png"
 ALT="$\displaystyle - \delta a \sin\mu.$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q_1+q_2+q_3+q_4+q_5=358.883+5.555-0.663-0.631-0.139+0.086=363.091^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="625" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1262.png"
 ALT="\begin{displaymath}
\lambda = \bar{\lambda} + q_1+q_2+q_3+q_4+q_5=358.883+5.555-0.663-0.631-0.139+0.086=
363.091^\circ,
\end{displaymath}">|; 

$key = q/+43^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="$+43^\circ 26'$">|; 

$key = q/14LE00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$14LE00$">|; 

$key = q/ZDS;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ZDS$">|; 

$key = q/164.041;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2056.png"
 ALT="$164.041$">|; 

$key = q/2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$2$">|; 

$key = q/displaystyle{{bf{n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle {\bf n}$">|; 

$key = q/2bar{D}-M_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1632.png"
 ALT="$2\bar{D}-M_M$">|; 

$key = q/S';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$S'$">|; 

$key = q/displaystylebar{lambda}-lambda_S,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1198.png"
 ALT="$\displaystyle \bar{\lambda} - \lambda_S,$">|; 

$key = q/+21';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1389.png"
 ALT="$+21'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere3.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere3.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashptol1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="526" HEIGHT="339" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/ptol1.eps}}
\end{figure}">|; 

$key = q/181.398;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1826.png"
 ALT="$181.398$">|; 

$key = q/bar{F}(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1234.png"
 ALT="$\bar{F}(^\circ)$">|; 

$key = q/e_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1459.png"
 ALT="$e_S$">|; 

$key = q/breve{n},(^circslash{{rm{day});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2143.png"
 ALT="$\breve{n} (^\circ/{\rm day})$">|; 

$key = q/-5^circ29';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="$ -5^\circ 29'$">|; 

$key = q/15';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="$15'$">|; 

$key = q/PiA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="$\Pi A$">|; 

$key = q/q=-0.712^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2112.png"
 ALT="$q= -0.712^\circ$">|; 

$key = q/{figure}{epsfysize{=2.75in{centerline{epsffile{epsfilesslashfig8.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="649" HEIGHT="313" BORDER="0"
 SRC="|."$dir".q|img1876.png"
 ALT="\begin{figure}
\epsfysize =2.75in
\centerline{\epsffile{epsfiles/fig8.eps}}
\end{figure}">|; 

$key = q/-6.588;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1279.png"
 ALT="$-6.588$">|; 

$key = q/varpi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="$\varpi$">|; 

$key = q/Msimeq237^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1966.png"
 ALT="$M\simeq 237^\circ$">|; 

$key = q/180^circ+lambda_c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$180^\circ+\lambda_c$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashphase.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="339" BORDER="0"
 SRC="|."$dir".q|img1449.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/phase.eps}}
\end{figure}">|; 

$key = q/{displaymath}deltah_-(114^circ)=-0.017,mbox{hspace{0.5cm}}bar{h}(114^circ)=1.056,mbox{hspace{0.5cm}}deltah_+(114^circ)=-0.027,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2065.png"
 ALT="\begin{displaymath}
\delta h_-(114^\circ) = -0.017,\mbox{\hspace{0.5cm}}\bar{h}(...
...c)=1.056, \mbox{\hspace{0.5cm}}\delta h_+(114^\circ) = -0.027,
\end{displaymath}">|; 

$key = q/q_{4'};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1566.png"
 ALT="$q_{4'}$">|; 

$key = q/CK=XL=(3slash2),e,a,sinM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="$CK = XL = (3/2) e a \sin M$">|; 

$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="$x$">|; 

$key = q/47.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1121.png"
 ALT="$47.8'$">|; 

$key = q/32';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="$32'$">|; 

$key = q/deltabeta_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1637.png"
 ALT="$\delta\beta_1$">|; 

$key = q/30';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="$30'$">|; 

$key = q/28.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1143.png"
 ALT="$28.6'$">|; 

$key = q/-720.471;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1922.png"
 ALT="$-720.471$">|; 

$key = q/48.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1139.png"
 ALT="$48.4'$">|; 

$key = q/00.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="$00.0'$">|; 

$key = q/displaystyleq;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="$\displaystyle q$">|; 

$key = q/displaystylecosmu;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$\displaystyle \cos \mu$">|; 

$key = q/314.268;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1964.png"
 ALT="$314.268$">|; 

$key = q/{displaymath}beta_0(4^circ)=0.173^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2093.png"
 ALT="\begin{displaymath}
\beta_0(4^\circ) = 0.173^\circ.
\end{displaymath}">|; 

$key = q/242^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$242^\circ$">|; 

$key = q/34.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1018.png"
 ALT="$34.4'$">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=-0.107times4.005-21.609-0.583times6.182=-25.642^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="572" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1975.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
... -0.107\times 4.005 -21.609-0.583\times 6.182 = -25.642^\circ.
\end{displaymath}">|; 

$key = q/12^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1367.png"
 ALT="$12^\circ 26'$">|; 

$key = q/Upsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="$\Upsilon$">|; 

$key = q/rho=QP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="$\rho=QP$">|; 

$key = q/181.455^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1800.png"
 ALT="$181.455^\circ$">|; 

$key = q/0^circ10';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2098.png"
 ALT="$0^\circ 10'$">|; 

$key = q/XY;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="$XY$">|; 

$key = q/R;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$R$">|; 

$key = q/Msimeq181^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1827.png"
 ALT="$M\simeq 181^\circ$">|; 

$key = q/XN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$XN$">|; 

$key = q/278.996;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1487.png"
 ALT="$278.996$">|; 

$key = q/GR;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$GR$">|; 

$key = q/28.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1137.png"
 ALT="$28.4'$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{108^circ01'{&{030^circ50'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="973" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $108^\circ 01'$&amp; $030^\circ 50'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/+8^circ29';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$+8^\circ 29'$">|; 

$key = q/{displaymath}beta_0(F)=sini,sinF{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2022.png"
 ALT="\begin{displaymath}
\beta_0(F) = \sin i \sin F
\end{displaymath}">|; 

$key = q/beta=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\beta = 0$">|; 

$key = q/44.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1007.png"
 ALT="$44.0'$">|; 

$key = q/sina=sinL,sinepsilon+cosL,cosepsilon,sinalpha_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\sin a = \sin L \sin \epsilon + \cos L \cos\epsilon \sin \alpha_0$">|; 

$key = q/{displaymath}Deltat=Deltaalpha(^circ)slash15^circ{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="\begin{displaymath}
\Delta t = \Delta\alpha(^\circ)/15^\circ
\end{displaymath}">|; 

$key = q/alpha_0=alpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\alpha_0=\alpha$">|; 

$key = q/C;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$C$">|; 

$key = q/19.388;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$19.388$">|; 

$key = q/-110.642;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1278.png"
 ALT="$-110.642$">|; 

$key = q/|beta_{syz}|<rho_U+rho_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1579.png"
 ALT="$ \vert\beta_{syz}\vert &lt; \rho_U+\rho_M$">|; 

$key = q/(180-136.3)slash0.61652137simeq71;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1954.png"
 ALT="$(180-136.3)/0.61652137\simeq
71$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q+theta.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1672.png"
 ALT="\begin{displaymath}
\lambda = \bar{\lambda} + q + \theta.
\end{displaymath}">|; 

$key = q/1.523706;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="$1.523706$">|; 

$key = q/37.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1096.png"
 ALT="$37.0'$">|; 

$key = q/G'P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1788.png"
 ALT="$G'P$">|; 

$key = q/105.253;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2118.png"
 ALT="$105.253$">|; 

$key = q/displaystyle{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\displaystyle {\bf r}$">|; 

$key = q/bar{lambda}_0,(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="$\bar{\lambda}_0 (^\circ)$">|; 

$key = q/+10';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1365.png"
 ALT="$+10'$">|; 

$key = q/310.749;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1483.png"
 ALT="$310.749$">|; 

$key = q/beta_{Mt}<|beta_{syz}|<beta_{M};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1608.png"
 ALT="$\beta_{Mt}&lt;\vert\beta_{syz}\vert&lt; \beta_{M}$">|; 

$key = q/M_0=317.857^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1873.png"
 ALT="$M_0 = 317.857^\circ$">|; 

$key = q/SC;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="$SC$">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=-0.355times0.126+9.212-0.125times0.129=9.151^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1910.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
... = -0.355\times 0.126 + 9.212-0.125\times 0.129 = 9.151^\circ.
\end{displaymath}">|; 

$key = q/a_5=2bar{F};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1227.png"
 ALT="$a_5=2\bar{F}$">|; 

$key = q/2tilde{D}-M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1435.png"
 ALT="$2\tilde{D}-M$">|; 

$key = q/204.617;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1960.png"
 ALT="$204.617$">|; 

$key = q/displaystyleF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1310.png"
 ALT="$\displaystyle F$">|; 

$key = q/-60^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$-60^\circ$">|; 

$key = q/CX;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$CX$">|; 

$key = q/RQ=a,sinE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="$RQ= a \sin E$">|; 

$key = q/+76^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$+76^\circ 34'$">|; 

$key = q/21^h07^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="$21^h07^m$">|; 

$key = q/delta_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1581.png"
 ALT="$\delta_M$">|; 

$key = q/{displaymath}rho_Ssimeqrho_{S,0},(1+e_S,cosM_S),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1551.png"
 ALT="\begin{displaymath}
\rho_S \simeq \rho_{S 0} (1+e_S \cos M_S),
\end{displaymath}">|; 

$key = q/e;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$e$">|; 

$key = q/29';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="$29'$">|; 

$key = q/0.03347795;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2154.png"
 ALT="$0.03347795$">|; 

$key = q/-0^circ23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="$-0^\circ 23'$">|; 

$key = q/56';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$56'$">|; 

$key = q/ZC;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1346.png"
 ALT="$ZC$">|; 

$key = q/Theta_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1734.png"
 ALT="$\Theta_+$">|; 

$key = q/zeta(M)=e,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1337.png"
 ALT="$\zeta (M)= e \cos M$">|; 

$key = q/49.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1169.png"
 ALT="$49.4'$">|; 

$key = q/mu=-1.267^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1937.png"
 ALT="$\mu = -1.267^\circ$">|; 

$key = q/Deltabar{F}_M(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1621.png"
 ALT="$\Delta \bar{F}_M(^\circ)$">|; 

$key = q/D;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$D$">|; 

$key = q/134.916;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1248.png"
 ALT="$134.916$">|; 

$key = q/lambdarightarrowlambda+180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$\lambda\rightarrow \lambda+180^\circ$">|; 

$key = q/bar{lambda}_0(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1420.png"
 ALT="$ \bar{\lambda}_0(^\circ)$">|; 

$key = q/+2.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1399.png"
 ALT="$+2.00$">|; 

$key = q/899.096;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1504.png"
 ALT="$899.096$">|; 

$key = q/displaystylee,cos,M-e^{,2},sin^2,M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1669.png"
 ALT="$\displaystyle e \cos M -e^{ 2} \sin^2 M,$">|; 

$key = q/41.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img923.png"
 ALT="$41.2'$">|; 

$key = q/{displaymath}deltatheta_-(22^circ)=0.126^circ,mbox{hspace{0.5cm}}bar{theta}(22^c{hspace{0.5cm}}deltatheta_+(22^circ)=0.129^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="454" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1904.png"
 ALT="\begin{displaymath}
\delta\theta_-(22^\circ) = 0.126^\circ,\mbox{\hspace{0.5cm}}...
..., \mbox{\hspace{0.5cm}}\delta\theta_+(22^\circ) = 0.129^\circ.
\end{displaymath}">|; 

$key = q/displaystyleT;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="$\displaystyle T$">|; 

$key = q/{displaymath}mu=lambda_S-bar{lambda}-q=44.602-196.501+0.091=-151.808simeq208^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="480" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1829.png"
 ALT="\begin{displaymath}
\mu=\lambda_S - \bar{\lambda}-q = 44.602-196.501 + 0.091= -151.808\simeq
208^\circ,
\end{displaymath}">|; 

$key = q/248^circ46'+39^circ00'=287^circ46';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$248^\circ 46' + 39^\circ00'=
287^\circ 46'$">|; 

$key = q/54.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1014.png"
 ALT="$54.2'$">|; 

$key = q/83.101;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1958.png"
 ALT="$83.101$">|; 

$key = q/+7^circ15';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$+7^\circ 15'$">|; 

$key = q/mu=360^circ-042^circ17'=317^circ43';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$\mu=360^\circ -042^\circ 17'=317^\circ 43'$">|; 

$key = q/{displaymath}mu=bar{lambda}+q-bar{lambda}_S=67.003-0.712-44.602=21.689simeq22^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1903.png"
 ALT="\begin{displaymath}
\mu=\bar{\lambda}+q-\bar{\lambda}_S = 67.003-0.712-44.602= 21.689\simeq
22^\circ.
\end{displaymath}">|; 

$key = q/19^circ22';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$19^\circ 22'$">|; 

$key = q/14.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1016.png"
 ALT="$14.4'$">|; 

$key = q/55.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1062.png"
 ALT="$55.8'$">|; 

$key = q/+11^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="$+11^\circ 34'$">|; 

$key = q/294.192;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1899.png"
 ALT="$294.192$">|; 

$key = q/14.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1028.png"
 ALT="$14.8'$">|; 

$key = q/317.857;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="$317.857$">|; 

$key = q/47.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1103.png"
 ALT="$47.2'$">|; 

$key = q/M_0,(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="$M_0 (^\circ)$">|; 

$key = q/{displaymath}rho_U=delta_M-rho_S.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1559.png"
 ALT="\begin{displaymath}
\rho_U = \delta_M-\rho_S.
\end{displaymath}">|; 

$key = q/t_0=2,451,545.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="$t_0= 2 451 545.0$">|; 

$key = q/bar{F}_0,(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2144.png"
 ALT="$\bar{F}_0 (^\circ)$">|; 

$key = q/t=;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$t=$">|; 

$key = q/0.042;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1824.png"
 ALT="$0.042$">|; 

$key = q/displaystylecosepsilon,{{bf{u}+sinepsilon,{{bf{p},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle \cos\epsilon {\bf u}+ \sin\epsilon {\bf p},$">|; 

$key = q/243.815;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1488.png"
 ALT="$243.815$">|; 

$key = q/beta_{Sa}(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1606.png"
 ALT="$\beta_{Sa}(')$">|; 

$key = q/mu>180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1727.png"
 ALT="$\mu &gt; 180^\circ$">|; 

$key = q/(1slash2),e,a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="$(1/2) e a$">|; 

$key = q/D=bar{D}+q_1+q_2+q_3+q_4+q_5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1474.png"
 ALT="$D=\bar{D} + q_1+q_2+q_3+q_4+q_5$">|; 

$key = q/1slash86,400;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="$1/86,400$">|; 

$key = q/displaystylefrac{cosepsilon,sinlambda,cosalpha_0-coslambda,sinalpha_0}{cosL,sineL,coslambda,cosalpha_0-sinL,cosepsilon,sinlambda,sinalpha_0}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="465" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle \frac{\cos\epsilon \sin\lambda \cos \alpha_0-\cos\lambda \sin ...
... \cos\lambda \cos \alpha_0-\sin L \cos\epsilon \sin\lambda \sin \alpha_0}.$">|; 

$key = q/xi=(bar{z}-z)slashdeltaz;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1731.png"
 ALT="$\xi = (\bar{z}-z)/\delta z$">|; 

$key = q/762.961;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="$762.961$">|; 

$key = q/{displaymath}tantheta=frac{sinmu}{rslashr'+cosmu},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1663.png"
 ALT="\begin{displaymath}
\tan\theta = \frac{\sin\mu}{r/r'+ \cos\mu},
\end{displaymath}">|; 

$key = q/18.4^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1999.png"
 ALT="$18.4^\circ$">|; 

$key = q/a_1=M_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1470.png"
 ALT="$a_1=M_M$">|; 

$key = q/Deltat=2445039.0-2451545.0=-6506.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1518.png"
 ALT="$\Delta t = 2445039.0 -2451545.0=-6506.0$">|; 

$key = q/displaystyle{{bf{e};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle {\bf e}$">|; 

$key = q/46.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1067.png"
 ALT="$46.0'$">|; 

$key = q/CR=a,cosE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="$CR= a \cos E$">|; 

$key = q/05.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1057.png"
 ALT="$05.8'$">|; 

$key = q/38.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1144.png"
 ALT="$38.6'$">|; 

$key = q/0.099;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1498.png"
 ALT="$0.099$">|; 

$key = q/56.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1074.png"
 ALT="$56.2'$">|; 

$key = q/15^circ5';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="$15^\circ 5'$">|; 

$key = q/53.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img984.png"
 ALT="$53.2'$">|; 

$key = q/{displaymath}{{bf{z}cdot{{bf{q}=sinL,cosepsilon-cosL,sinepsilon,sin(alpha-t).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="\begin{displaymath}
{\bf z}\cdot{\bf q} = \sin L \cos\epsilon - \cos L \sin\epsilon \sin(\alpha-t).
\end{displaymath}">|; 

$key = q/LT=UT-phi(^circ)slash15^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="$LT = UT- \phi(^\circ)/15^\circ$">|; 

$key = q/Pi';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1651.png"
 ALT="$\Pi'$">|; 

$key = q/^nomath_inline{dagnomath_inline{;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="$^\dag $">|; 

$key = q/238.494;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1239.png"
 ALT="$238.494$">|; 

$key = q/{displaymath}q(354^circ)=-0.204^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="\begin{displaymath}
q(354^\circ)= -0.204^\circ,
\end{displaymath}">|; 

$key = q/120.001;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="$120.001$">|; 

$key = q/{displaymath}a_1=M_Msimeq179^circ,~~~a_2=2bar{D}-M_M=2times357.813-179.082simeq177^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="519" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1509.png"
 ALT="\begin{displaymath}
a_1=M_M\simeq 179^\circ,&nbsp;&nbsp;&nbsp;a_2=2\bar{D}-M_M = 2\times 357.813-179.082\simeq 177^\circ,
\end{displaymath}">|; 

$key = q/beta_{Sa}>beta_{St};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1599.png"
 ALT="$\beta_{Sa}&gt;\beta_{St}$">|; 

$key = q/M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$M$">|; 

$key = q/83.139;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1957.png"
 ALT="$83.139$">|; 

$key = q/displaystylecosL,{{bf{p}-sinL,{{bf{m},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle \cos L {\bf p} - \sin L {\bf m},$">|; 

$key = q/30.133;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1843.png"
 ALT="$30.133$">|; 

$key = q/{{bf{m};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="${\bf m}$">|; 

$key = q/displaystyle+sinL,sinepsilon,sinalpha_0),{{bf{q},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\displaystyle +\sin L \sin \epsilon \sin \alpha_0) {\bf q},$">|; 

$key = q/23^circ24';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$23^\circ 24'$">|; 

$key = q/2,e,a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img680.png"
 ALT="$2 e a$">|; 

$key = q/+15^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="$+15^\circ 00'$">|; 

$key = q/33.508;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1840.png"
 ALT="$33.508$">|; 

$key = q/M(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="$M(^\circ)$">|; 

$key = q/-134.675;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1524.png"
 ALT="$-134.675$">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=0.469times0.447-6.194+0.121times0.522=-5.921^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1836.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
..._+ = 0.469\times 0.447-6.194+0.121\times 0.522 =- 5.921^\circ.
\end{displaymath}">|; 

$key = q/57';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="$57'$">|; 

$key = q/0.723334;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="$0.723334$">|; 

$key = q/F=bar{F}_M+q_1+q_2+q_3+q_{4'}+q_5=63.139+6.239-1.320+0.119-0.145-0.097=67.926simeq68^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="748" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1574.png"
 ALT="$F = \bar{F}_M + q_1+q_2+q_3+q_{4'}+q_5
=63.139+6.239-1.320+0.119-0.145-0.097=67.926\simeq 68^\circ$">|; 

$key = q/^s;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1193.png"
 ALT="$^s$">|; 

$key = q/GV;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$GV$">|; 

$key = q/2445039.0+(180.00-187.90)slash12.1907491=2445038.35;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1545.png"
 ALT="$2445039.0 +(180.00-187.90)/12.1907491= 2445038.35$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="\begin{displaymath}
\lambda = \bar{\lambda} + q,
\end{displaymath}">|; 

$key = q/PP';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$PP'$">|; 

$key = q/02^circ56';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="$02^\circ 56'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashpara.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img1344.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/para.eps}}
\end{figure}">|; 

$key = q/|beta_{syz}|<beta_{St};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1594.png"
 ALT="$\vert\beta_{syz}\vert&lt;\beta_{St}$">|; 

$key = q/q_5=-0.097^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1572.png"
 ALT="$q_5=-0.097^\circ$">|; 

$key = q/338.757;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1238.png"
 ALT="$338.757$">|; 

$key = q/-153.601;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1521.png"
 ALT="$-153.601$">|; 

$key = q/10.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="$10.4'$">|; 

$key = q/52.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img954.png"
 ALT="$52.2'$">|; 

$key = q/51.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img936.png"
 ALT="$51.6'$">|; 

$key = q/02.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img955.png"
 ALT="$02.4'$">|; 

$key = q/+1.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$+1.9$">|; 

$key = q/textstyleequiv;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$\textstyle \equiv$">|; 

$key = q/GUpsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1301.png"
 ALT="$G\Upsilon$">|; 

$key = q/12;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$12$">|; 

$key = q/bar{lambda};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="$\bar{\lambda}$">|; 

$key = q/164.021;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1743.png"
 ALT="$164.021$">|; 

$key = q/47.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1097.png"
 ALT="$47.0'$">|; 

$key = q/+56';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1364.png"
 ALT="$+56'$">|; 

$key = q/11.7%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1617.png"
 ALT="$11.7\%$">|; 

$key = q/-7^circ11';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$-7^\circ 11'$">|; 

$key = q/q_4(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1433.png"
 ALT="$q_4(^\circ)$">|; 

$key = q/90^circ-|L|;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$90^\circ - \vert L\vert$">|; 

$key = q/40.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="$40.4'$">|; 

$key = q/22.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img963.png"
 ALT="$22.6'$">|; 

$key = q/68^circ32';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1392.png"
 ALT="$68^\circ 32'$">|; 

$key = q/Msimeq120^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="$M\simeq 120^\circ$">|; 

$key = q/23^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$23^\circ$">|; 

$key = q/13.22935027;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1424.png"
 ALT="$13.22935027$">|; 

$key = q/{displaymath}beta_{St}=56.59'+deltabeta_1(M_M)+deltabeta_2(M_M)-deltabeta_3(M_S),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1596.png"
 ALT="\begin{displaymath}
\beta_{St} = 56.59' + \delta\beta_1(M_M)+\delta\beta_2 (M_M)-\delta\beta_3(M_S),
\end{displaymath}">|; 

$key = q/z_{{rm{max};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1698.png"
 ALT="$z_{\rm max}$">|; 

$key = q/27.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1113.png"
 ALT="$27.6'$">|; 

$key = q/07^circ48';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$07^\circ 48'$">|; 

$key = q/59.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1158.png"
 ALT="$59.0'$">|; 

$key = q/breve{n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1215.png"
 ALT="$\breve{n}$">|; 

$key = q/357.813;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1505.png"
 ALT="$357.813$">|; 

$key = q/GN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1302.png"
 ALT="$GN$">|; 

$key = q/M=90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1358.png"
 ALT="$M=90^\circ$">|; 

$key = q/eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$\eta$">|; 

$key = q/10.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="$10.0'$">|; 

$key = q/26^circ37';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1372.png"
 ALT="$26^\circ 37'$">|; 

$key = q/-79.376;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1528.png"
 ALT="$-79.376$">|; 

$key = q/|beta_{syz}|<beta_{Sa};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1598.png"
 ALT="$\vert\beta_{syz}\vert&lt;\beta_{Sa}$">|; 

$key = q/displaystylebar{z}=frac{1+e,e'}{1-e'^{,2}},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1678.png"
 ALT="$\displaystyle \bar{z} = \frac{1+e e'}{1-e'^{ 2}},$">|; 

$key = q/{displaymath}F=bar{F}+q,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2013.png"
 ALT="\begin{displaymath}
F = \bar{F} + q,
\end{displaymath}">|; 

$key = q/PCKL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="$PCKL$">|; 

$key = q/displaystyleq_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1201.png"
 ALT="$\displaystyle q_2$">|; 

$key = q/displaystyle{{bf{m};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle {\bf m}$">|; 

$key = q/UU';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$UU'$">|; 

$key = q/M_0=19.388^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1865.png"
 ALT="$M_0 = 19.388^\circ$">|; 

$key = q/bar{F}_0=293.660^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1871.png"
 ALT="$\bar{F}_0=293.660^\circ$">|; 

$key = q/displaystylebar{lambda}_0+n,(t-t_0),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="$\displaystyle \bar{\lambda}_0+ n (t-t_0),$">|; 

$key = q/72^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$72^\circ$">|; 

$key = q/XCKL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="$XCKL$">|; 

$key = q/i(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1423.png"
 ALT="$i(^\circ)$">|; 

$key = q/displaystylebar{lambda}+q-bar{lambda}_S,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2107.png"
 ALT="$\displaystyle \bar{\lambda}+q-\bar{\lambda}_S,$">|; 

$key = q/deltabeta_2(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1635.png"
 ALT="$\delta\beta_2(')$">|; 

$key = q/{displaymath}z=(1-zeta)slash(1-zeta_S)=(1+5.45times10^{-3})slash(1-1.662times10^{-2})=1.02244,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1782.png"
 ALT="\begin{displaymath}
z= (1-\zeta)/(1-\zeta_S) = (1+5.45\times 10^{-3})/(1-1.662\times 10^{-2}) =
1.02244,
\end{displaymath}">|; 

$key = q/{displaymath}tsimeqt_0+552-8.649slash0.46157617simeqt_0+533,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1799.png"
 ALT="\begin{displaymath}
t\simeq t_0 +552-8.649/0.46157617\simeq t_0+533 {\rm JD}.
\end{displaymath}">|; 

$key = q/rho_S=R_Sslashr_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1546.png"
 ALT="$\rho_S = R_S/r_S$">|; 

$key = q/51.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img930.png"
 ALT="$51.4'$">|; 

$key = q/44^circ36';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="$44^\circ36'$">|; 

$key = q/SW=SL+LW=SL+XZ=a-e,a,cos,M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="$SW = SL+LW=SL+XZ= a-e a \cos M$">|; 

$key = q/Theta_+(xi)=-Theta_-(-xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1736.png"
 ALT="$\Theta_+(\xi)=-\Theta_-(-\xi)$">|; 

$key = q/musimeq253^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2138.png"
 ALT="$\mu\simeq 253^\circ$">|; 

$key = q/iota;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$\iota$">|; 

$key = q/264.587;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1489.png"
 ALT="$264.587$">|; 

$key = q/{displaymath}a_1=Msimeq114^circ,~~~a_2=2tilde{D}-M=-2times253.580-114.047=-621.207simeq99^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="563" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1289.png"
 ALT="\begin{displaymath}
a_1=M\simeq 114^\circ,&nbsp;&nbsp;&nbsp;a_2=2\tilde{D}-M = -2\times 253.580-114.047=-621.207 \simeq 99^\circ,
\end{displaymath}">|; 

$key = q/044^circ29';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1403.png"
 ALT="$044^\circ 29'$">|; 

$key = q/43.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1001.png"
 ALT="$43.8'$">|; 

$key = q/16.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1088.png"
 ALT="$16.8'$">|; 

$key = q/48.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1151.png"
 ALT="$48.8'$">|; 

$key = q/+51';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1374.png"
 ALT="$+51'$">|; 

$key = q/361.781;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2090.png"
 ALT="$361.781$">|; 

$key = q/bar{a}=a,bar{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1808.png"
 ALT="$\bar{a} = a \bar{z}$">|; 

$key = q/r,sinT=b,sinE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="$r \sin T = b \sin E$">|; 

$key = q/{displaymath}{{bf{P}={{bf{S}+{{bf{P}'equiv{{bf{P}'+{{bf{S}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1643.png"
 ALT="\begin{displaymath}
{\bf P} = {\bf S}+{\bf P}' \equiv{\bf P}'+{\bf S}.
\end{displaymath}">|; 

$key = q/+2.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="$+2.9$">|; 

$key = q/07.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1117.png"
 ALT="$07.8'$">|; 

$key = q/{displaymath}F=bar{F}+q=350.223-0.712=349.511simeq350^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2120.png"
 ALT="\begin{displaymath}
F = \bar{F} + q = 350.223-0.712 = 349.511\simeq 350^\circ.
\end{displaymath}">|; 

$key = q/{displaymath}t=t_0+452+1.100slash0.61652137=t_0+453.8,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1941.png"
 ALT="\begin{displaymath}
t = t_0 +452+1.100/0.61652137 = t_0+453.8 {\rm JD},
\end{displaymath}">|; 

$key = q/+25^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="$+25^\circ$">|; 

$key = q/bar{lambda}(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="$ \bar{\lambda}(^\circ)$">|; 

$key = q/RP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="$RP$">|; 

$key = q/09.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1153.png"
 ALT="$09.0'$">|; 

$key = q/0.08308100;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="$0.08308100$">|; 

$key = q/{displaymath}r,sinT=b,sinE=a,(1-e^2)^{1slash2},sinE.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="\begin{displaymath}
r \sin T = b \sin E = a (1-e^2)^{1/2} \sin E.
\end{displaymath}">|; 

$key = q/{displaymath}delta_M=frac{R_E}{r_M}=delta_{M,0},(1+e_M,cosM_M),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1556.png"
 ALT="\begin{displaymath}
\delta_M = \frac{R_E}{r_M}= \delta_{M 0} (1+e_M \cos M_M),
\end{displaymath}">|; 

$key = q/^S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="$^\S$">|; 

$key = q/alpha_0=-sin^{-1}(tanL,tanepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\alpha_0=-\sin^{-1}(\tan L \tan\epsilon)$">|; 

$key = q/+30^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="$+30^\circ 00'$">|; 

$key = q/displaystyleM+2,e,sinM+e^2,sin2M.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="$\displaystyle M + 2 e \sin M + e^2 \sin 2M.$">|; 

$key = q/297.864;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1500.png"
 ALT="$297.864$">|; 

$key = q/DB;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1345.png"
 ALT="$DB$">|; 

$key = q/F(mu,z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2026.png"
 ALT="$F(\mu,z)$">|; 

$key = q/52.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img948.png"
 ALT="$52.0'$">|; 

$key = q/4.09234221;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2146.png"
 ALT="$4.09234221$">|; 

$key = q/23^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="$23^\circ 26'$">|; 

$key = q/{displaymath}deltaa=delta(a),[1+zeta(M)],{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1334.png"
 ALT="\begin{displaymath}
\delta a = \delta (a) [1+\zeta (M)],
\end{displaymath}">|; 

$key = q/U;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$U$">|; 

$key = q/CS=e,a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$CS = e a$">|; 

$key = q/00.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="$00.6'$">|; 

$key = q/33.478;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2087.png"
 ALT="$33.478$">|; 

$key = q/Msimeq23^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1850.png"
 ALT="$M\simeq 23^\circ$">|; 

$key = q/06^circ19';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="$06^\circ 19'$">|; 

$key = q/bar{F}_{M,0}=93.284^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1629.png"
 ALT="$\bar{F}_{M 0} = 93.284^\circ$">|; 

$key = q/01.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img937.png"
 ALT="$01.8'$">|; 

$key = q/54.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1032.png"
 ALT="$54.8'$">|; 

$key = q/03^circ11';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="$03^\circ 11'$">|; 

$key = q/displaystyleh(mu,bar{z})-h(mu,z_{{rm{max}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2033.png"
 ALT="$\displaystyle h(\mu,\bar{z}) - h(\mu,z_{\rm max}),$">|; 

$key = q/lambda_c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$\lambda_c$">|; 

$key = q/M_0=19.348^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1870.png"
 ALT="$M_0 = 19.348^\circ$">|; 

$key = q/21.7^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1979.png"
 ALT="$21.7^\circ$">|; 

$key = q/1.924;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2117.png"
 ALT="$1.924$">|; 

$key = q/a_4=M_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1226.png"
 ALT="$a_4 = M_S$">|; 

$key = q/21.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img933.png"
 ALT="$21.6'$">|; 

$key = q/-314.443;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1769.png"
 ALT="$-314.443$">|; 

$key = q/-241.278;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1918.png"
 ALT="$-241.278$">|; 

$key = q/t=t_h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$t=t_h$">|; 

$key = q/M_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1462.png"
 ALT="$M_M$">|; 

$key = q/27.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1101.png"
 ALT="$27.2'$">|; 

$key = q/00.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img907.png"
 ALT="$00.8'$">|; 

$key = q/02.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img949.png"
 ALT="$02.2'$">|; 

$key = q/GBP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$GBP$">|; 

$key = q/{displaymath}Deltaalpha=bar{alpha}-alpha=lambda-tan^{-1}(cosepsilon,tanlambda)-2,e,sin,M,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="\begin{displaymath}
\Delta\alpha = \bar{\alpha}-\alpha = \lambda - \tan^{-1}(\cos \epsilon \tan\lambda) - 2 e \sin M,
\end{displaymath}">|; 

$key = q/57.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1116.png"
 ALT="$57.6'$">|; 

$key = q/+03';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1375.png"
 ALT="$+03'$">|; 

$key = q/displaystyle-sinepsilon,{{bf{u}+cosepsilon,{{bf{p},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle -\sin \epsilon {\bf u} + \cos\epsilon {\bf p},$">|; 

$key = q/54';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="$54'$">|; 

$key = q/{displaymath}t=t_0+265.2,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="\begin{displaymath}
t = t_0+265.2 {\rm JD},
\end{displaymath}">|; 

$key = q/q_{4'}(M_S)=-0.145^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1573.png"
 ALT="$q_{4'}(M_S) = -0.145^\circ$">|; 

$key = q/L=+23^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$L=+23^\circ 26'$">|; 

$key = q/Theta_+=-0.121;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2072.png"
 ALT="$\Theta_+ = -0.121$">|; 

$key = q/bar{theta}(360^circ-mu)=-bar{theta}(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1729.png"
 ALT="$\bar{\theta}(360^\circ - \mu) =-\bar{\theta}(\mu)$">|; 

$key = q/27.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2008.png"
 ALT="$27.3^\circ$">|; 

$key = q/{displaymath}tilde{D}=bar{lambda}-lambda_S=19.475-273.055=-253.580^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1288.png"
 ALT="\begin{displaymath}
\tilde{D}=\bar{\lambda}-\lambda_S = 19.475-273.055 = -253.580^\circ.
\end{displaymath}">|; 

$key = q/20^circ14';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$20^\circ 14'$">|; 

$key = q/17^circ20';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$17^\circ 20'$">|; 

$key = q/displaystyle{{bf{r}cdot{{bf{z},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle {\bf r}\cdot {\bf z},$">|; 

$key = q/+75^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$+75^\circ $">|; 

$key = q/55.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1044.png"
 ALT="$55.2'$">|; 

$key = q/2.6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$2.6$">|; 

$key = q/{displaymath}musimeqbar{mu}=bar{lambda}-bar{lambda}_S=bar{lambda}_0-bar{lambda}_0,S}+(n-n_S),(t-t_0)=261.515+0.61652137,(t-t_0).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1935.png"
 ALT="\begin{displaymath}
\mu \simeq \bar{\mu} = \bar{\lambda}-\bar{\lambda}_S = \bar{...
...da}_{0 S} +
(n-n_S) (t-t_0) = 261.515 + 0.61652137 (t-t_0).
\end{displaymath}">|; 

$key = q/09.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1165.png"
 ALT="$09.4'$">|; 

$key = q/{displaymath}lambda=bar{lambda}_S+theta=44.602+9.151=53.753simeq53^circ45'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1911.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda}_S + \theta= 44.602+9.151=53.753 \simeq 53^\circ 45'.
\end{displaymath}">|; 

$key = q/16^h09^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="$16^h09^m$">|; 

$key = q/-269.958;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1522.png"
 ALT="$-269.958$">|; 

$key = q/28.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1131.png"
 ALT="$28.2'$">|; 

$key = q/CBequivb=a,(1-e^2)^{1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="$CB\equiv b = a (1-e^2)^{1/2}$">|; 

$key = q/56.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1068.png"
 ALT="$56.0'$">|; 

$key = q/mu=125.6^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1838.png"
 ALT="$\mu=125.6^\circ$">|; 

$key = q/aequivCY;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$a\equiv CY$">|; 

$key = q/1078.883;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1250.png"
 ALT="$1078.883$">|; 

$key = q/0.52402076;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="$0.52402076$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashcop1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="569" HEIGHT="338" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/cop1.eps}}
\end{figure}">|; 

$key = q/deltaa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1329.png"
 ALT="$\delta a$">|; 

$key = q/{displaymath}|beta_{syz}|<delta_M+rho_M+rho_S.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1586.png"
 ALT="\begin{displaymath}
\vert\beta_{syz}\vert&lt; \delta_M + \rho_M + \rho_S.
\end{displaymath}">|; 

$key = q/GG';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1656.png"
 ALT="$GG'$">|; 

$key = q/12.37times0.117simeq1.4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1619.png"
 ALT="$12.37\times 0.117\simeq 1.4$">|; 

$key = q/displaystyletan,alpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle \tan \alpha$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashlong.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img2024.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/long.eps}}
\end{figure}">|; 

$key = q/displaystyle{{rm{Area},SRP+{{rm{Area},PiRP=frac{1}{2},r^2,cosT,sinT+{{rm{Area},PiRP.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="$\displaystyle {\rm Area}  SRP + {\rm Area}  \Pi RP
= \frac{1}{2} r^2 \cos T \sin T + {\rm Area} \Pi RP.$">|; 

$key = q/-0.493;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="$-0.493$">|; 

$key = q/20';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="$20'$">|; 

$key = q/a'=a-deltaa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1325.png"
 ALT="$a' = a-\delta a$">|; 

$key = q/displaystylee,cosM-e^2,sin^2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1701.png"
 ALT="$\displaystyle e \cos M - e^2 \sin^2 M,$">|; 

$key = q/{displaymath}tsimeqt_0+(360-280.458)slash0.98564735simeqt_0+81,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="\begin{displaymath}
t \simeq t_0+(360-280.458)/0.98564735 \simeq t_0+81 {\rm JD}.
\end{displaymath}">|; 

$key = q/displaystylecosL,coslambda,cosalpha_0+sinL,sinepsilon,sinlambda+cosL,cosepsilon,sinlambda,sinalpha_0,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="463" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\displaystyle \cos L \cos\lambda \cos \alpha_0+ \sin L \sin\epsilon \sin \lambda
+ \cos L \cos\epsilon \sin\lambda \sin \alpha_0,$">|; 

$key = q/-52.496;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1526.png"
 ALT="$-52.496$">|; 

$key = q/F=bar{F}+q_1+q_2+q_3+q_4+q_5=337.132+5.555-0.663-0.631-0.139+0.086simeq341^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="677" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1321.png"
 ALT="$F=\bar{F}+q_1+q_2+q_3+q_4+q_5
=337.132+5.555-0.663-0.631-0.139+0.086\simeq 341^\circ$">|; 

$key = q/13';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="$13'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashhipp1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="569" HEIGHT="338" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/hipp1.eps}}
\end{figure}">|; 

$key = q/displaystylecosepsilon,tanlambda.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \cos\epsilon \tan\lambda.$">|; 

$key = q/a_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1228.png"
 ALT="$a_1$">|; 

$key = q/z=(1-zeta_S)slash(1-zeta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1890.png"
 ALT="$z = (1-\zeta_S)/(1-\zeta)$">|; 

$key = q/48.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1133.png"
 ALT="$48.2'$">|; 

$key = q/223.7^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1951.png"
 ALT="$223.7^\circ$">|; 

$key = q/a=44^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1338.png"
 ALT="$a=44^\circ 00'$">|; 

$key = q/22';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="$22'$">|; 

$key = q/{displaymath}lambdasimeqbar{lambda}=bar{lambda}_0+n,(t-t_0)=280.458+0.98564735,(t-t_0),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="\begin{displaymath}
\lambda\simeq \bar{\lambda} = \bar{\lambda}_0 + n (t-t_0)
= 280.458 + 0.98564735 (t-t_0),
\end{displaymath}">|; 

$key = q/296.482;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2089.png"
 ALT="$296.482$">|; 

$key = q/13.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img992.png"
 ALT="$13.6'$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{epsfilesslashfig1.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="485" HEIGHT="278" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{epsfiles/fig1.eps}}
\end{figure}">|; 

$key = q/displaystyletheta(mu,bar{z})equivtan^{-1}left(frac{sinmu}{a,bar{z}+cosmu}right),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1705.png"
 ALT="$\displaystyle \theta(\mu,\bar{z})\equiv \tan^{-1} \left(\frac{\sin\mu}{a \bar{z}+\cos\mu}\right),$">|; 

$key = q/35';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$35'$">|; 

$key = q/-95.849;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1277.png"
 ALT="$-95.849$">|; 

$key = q/a=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$a=0$">|; 

$key = q/12.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img956.png"
 ALT="$12.4'$">|; 

$key = q/displaystylefrac{1-zeta}{1-zeta_S},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1709.png"
 ALT="$\displaystyle \frac{1-\zeta}{1-\zeta_S},$">|; 

$key = q/{displaymath}beta_0(250^circ)=-2.511^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2137.png"
 ALT="\begin{displaymath}
\beta_0(250^\circ) = -2.511^\circ.
\end{displaymath}">|; 

$key = q/YP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="$YP$">|; 

$key = q/-20';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1394.png"
 ALT="$-20'$">|; 

$key = q/-90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$-90^\circ$">|; 

$key = q/lambda=270^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="$\lambda = 270^\circ$">|; 

$key = q/G';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1644.png"
 ALT="$G'$">|; 

$key = q/VV';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$VV'$">|; 

$key = q/bar{z}=1.04774;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1971.png"
 ALT="$\bar{z}= 1.04774$">|; 

$key = q/beta_{St}>beta_{Sa};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1595.png"
 ALT="$\beta_{St}&gt;\beta_{Sa}$">|; 

$key = q/2444994.7+1.5times29.53simeq2445039.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1517.png"
 ALT="$2444994.7
+ 1.5\times 29.53\simeq 2445039.0$">|; 

$key = q/24.2^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1995.png"
 ALT="$24.2^\circ$">|; 

$key = q/{displaymath}a_5=2bar{F}_M=2times63.062simeq126^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1540.png"
 ALT="\begin{displaymath}
a_5=2\bar{F}_M = 2\times 63.062\simeq 126^\circ.
\end{displaymath}">|; 

$key = q/{displaymath}h=Theta_-,deltah_-+bar{h}+Theta_+,deltah_+=-0.071times0.002+0.966-0.759times0.003=0.964.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2096.png"
 ALT="\begin{displaymath}
h = \Theta_- \delta h_- + \bar{h}+\Theta_+ \delta h_+ = -0.071\times 0.002 +0.966-0.759\times 0.003 = 0.964.
\end{displaymath}">|; 

$key = q/M_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="$M_0$">|; 

$key = q/17.610;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1485.png"
 ALT="$17.610$">|; 

$key = q/displaystyletilde{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1197.png"
 ALT="$\displaystyle \tilde{D}$">|; 

$key = q/23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="$23'$">|; 

$key = q/tilde{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1436.png"
 ALT="$\tilde{D}$">|; 

$key = q/{displaymath}frac{r}{a}=(1-2,e,cosM+e^2+3,e^2,sin^2M)^{1slash2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="\begin{displaymath}
\frac{r}{a} = (1-2 e \cos M +e^2+3 e^2 \sin^2 M)^{1/2}.
\end{displaymath}">|; 

$key = q/09.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1159.png"
 ALT="$09.2'$">|; 

$key = q/alpha_0=alpha-90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$\alpha_0=\alpha-90^\circ$">|; 

$key = q/lambda=bar{lambda}+q_1+q_2+q_3+q_4+q_5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1230.png"
 ALT="$\lambda=\bar{\lambda} + q_1+q_2+q_3+q_4+q_5$">|; 

$key = q/{displaymath}bar{alpha}=bar{lambda},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="\begin{displaymath}
\bar{\alpha} = \bar{\lambda},
\end{displaymath}">|; 

$key = q/-14';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1390.png"
 ALT="$-14'$">|; 

$key = q/32.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img958.png"
 ALT="$32.4'$">|; 

$key = q/t_ast;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="$t_\ast$">|; 

$key = q/33.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img994.png"
 ALT="$33.6'$">|; 

$key = q/+12^circ36';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$+12^\circ 36'$">|; 

$key = q/bar{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1717.png"
 ALT="$\bar{z}$">|; 

$key = q/tilde{n},(^circslash{{rm{day});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="$\tilde{n} (^\circ/{\rm day})$">|; 

$key = q/180^circleqmuleq360^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$180^\circ\leq \mu\leq 360^\circ$">|; 

$key = q/varpi_1=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="$\varpi_1=0$">|; 

$key = q/{displaymath}beta_0(F)=a,sini,sinF{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2103.png"
 ALT="\begin{displaymath}
\beta_0(F) = a \sin i \sin F
\end{displaymath}">|; 

$key = q/{displaymath}|beta_{syz}|<delta_M-rho_M-rho_S,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1578.png"
 ALT="\begin{displaymath}
\vert\beta_{syz}\vert &lt; \delta_M-\rho_M-\rho_S,
\end{displaymath}">|; 

$key = q/M_M(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1482.png"
 ALT="$M_M(^\circ)$">|; 

$key = q/displaystyleM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="$\displaystyle M$">|; 

$key = q/+9^circ43';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$+9^\circ 43'$">|; 

$key = q/08.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1123.png"
 ALT="$08.0'$">|; 

$key = q/-296.869;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1532.png"
 ALT="$-296.869$">|; 

$key = q/04.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1009.png"
 ALT="$04.2'$">|; 

$key = q/{displaymath}q_4(a_4)=-1.896^circ,~~q_5(a_5)=-0.097^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1542.png"
 ALT="\begin{displaymath}q_4(a_4)=-1.896^\circ,&nbsp;&nbsp;q_5(a_5)= -0.097^\circ.
\end{displaymath}">|; 

$key = q/displaystylesinbeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle \sin\beta$">|; 

$key = q/+61^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="$+61^\circ 34'$">|; 

$key = q/displaystyleM_0+tilde{n},(t-t_0),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="$\displaystyle M_0 + \tilde{n} (t-t_0),$">|; 

$key = q/05.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1045.png"
 ALT="$05.4'$">|; 

$key = q/SR=r,cosT;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="$SR=r \cos T$">|; 

$key = q/2453174.10+(360.00-357.22)slash12.1907491=2453174.33;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1516.png"
 ALT="$2453174.10 +(360.00-357.22)/12.1907491= 2453174.33$">|; 

$key = q/QK=PL=2,e,a,sinM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$QK = PL = 2 e a \sin M$">|; 

$key = q/+9^circ40';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="$+9^\circ 40'$">|; 

$key = q/34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="$34'$">|; 

$key = q/M_0=134.916^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1428.png"
 ALT="$M_0 = 134.916^\circ$">|; 

$key = q/32.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img970.png"
 ALT="$32.8'$">|; 

$key = q/58';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="$58'$">|; 

$key = q/35.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1060.png"
 ALT="$35.8'$">|; 

$key = q/-0.801;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1921.png"
 ALT="$-0.801$">|; 

$key = q/deltaz=(e+e_S)slash(1-e^{,2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1885.png"
 ALT="$\delta z = (e+e_S)/(1-e^{ 2})$">|; 

$key = q/{displaymath}M_0=bar{lambda}_0-varpi_0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="\begin{displaymath}
M_0 = \bar{\lambda}_0 - \varpi_0
\end{displaymath}">|; 

$key = q/778.185;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1251.png"
 ALT="$778.185$">|; 

$key = q/83.081;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1819.png"
 ALT="$83.081$">|; 

$key = q/204.619;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1959.png"
 ALT="$204.619$">|; 

$key = q/displaystylebar{D}+q_1+q_2+q_3+q_4+q_5.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1458.png"
 ALT="$\displaystyle \bar{D} + q_1+q_2+q_3+q_4+q_5.$">|; 

$key = q/29^circ37';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="$29^\circ 37'$">|; 

$key = q/180;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$180$">|; 

$key = q/displaystyle-cosL,sinepsilon,sinalpha_0),{{bf{q}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle -\cos L \sin\epsilon \sin \alpha_0) {\bf q}.$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q_1+q_2+q_3+q_4+q_5=19.475+5.562+1.311-0.394+0.017-0.021=25.950^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="608" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1294.png"
 ALT="\begin{displaymath}
\lambda = \bar{\lambda} + q_1+q_2+q_3+q_4+q_5=19.475+5.562+1.311-0.394+0.017-0.021=
25.950^\circ,
\end{displaymath}">|; 

$key = q/{displaymath}sindeltaa=frac{R}{r},cosa'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1326.png"
 ALT="\begin{displaymath}
\sin \delta a = \frac{R}{r} \cos a'.
\end{displaymath}">|; 

$key = q/11^circ28';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$11^\circ 28'$">|; 

$key = q/40.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="$40.8'$">|; 

$key = q/00^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$00^\circ 00'$">|; 

$key = q/00.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="$00.4'$">|; 

$key = q/bar{theta}=pm46.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1952.png"
 ALT="$\bar{\theta} = \pm 46.3^\circ$">|; 

$key = q/-8^circ12';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="$-8^\circ 12'$">|; 

$key = q/NESW;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$NESW$">|; 

$key = q/displaystyleh(mu,z_{{rm{min})-h(mu,bar{z}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2035.png"
 ALT="$\displaystyle h(\mu,z_{\rm min}) - h(\mu,\bar{z}),$">|; 

$key = q/4.154;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1823.png"
 ALT="$4.154$">|; 

$key = q/displaystylebar{h};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2030.png"
 ALT="$\displaystyle \bar{h}$">|; 

$key = q/{figure}{epsfysize{=2.75in{centerline{epsffile{epsfilesslashfigv7.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="746" HEIGHT="314" BORDER="0"
 SRC="|."$dir".q|img1645.png"
 ALT="\begin{figure}
\epsfysize =2.75in
\centerline{\epsffile{epsfiles/figv7.eps}}
\end{figure}">|; 

$key = q/displaystyle{{bf{p};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle {\bf p}$">|; 

$key = q/displaystyleleft(frac{{{bf{r}cdot{{bf{u}}{{{bf{r}cdot{{bf{v}}right).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle \left(\frac{{\bf r}\cdot{\bf u}}{{\bf r}\cdot {\bf v}}\right).$">|; 

$key = q/displaystyle-sinL,cosalpha_0,{{bf{v}-sinL,sinalpha_0,{{bf{u}+cosL,{{bf{p},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle -\sin L \cos \alpha_0 {\bf v} - \sin L \sin \alpha_0 {\bf u} + \cos L {\bf p},$">|; 

$key = q/{displaymath}D=lambda_M-lambda_S.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1445.png"
 ALT="\begin{displaymath}
D = \lambda_M - \lambda_S.
\end{displaymath}">|; 

$key = q/+50^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$+50^\circ $">|; 

$key = q/|L-delta|>90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$\vert L-\delta\vert&gt;90^\circ$">|; 

$key = q/D=180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1448.png"
 ALT="$D = 180^\circ$">|; 

$key = q/^ast68;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="$^\ast 68$">|; 

$key = q/19.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1178.png"
 ALT="$19.8'$">|; 

$key = q/mu=180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1789.png"
 ALT="$\mu=180^\circ$">|; 

$key = q/q_3=0.119^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1571.png"
 ALT="$q_3=0.119^\circ$">|; 

$key = q/Lrightarrow-L;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$L\rightarrow -L$">|; 

$key = q/{displaymath}M=bar{lambda}+M_0-bar{lambda}_0=bar{lambda}+77.213^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="\begin{displaymath}
M = \bar{\lambda} + M_0-\bar{\lambda}_0 = \bar{\lambda} +77.213^\circ.
\end{displaymath}">|; 

$key = q/deltaz=0.23216;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1972.png"
 ALT="$\delta z = 0.23216$">|; 

$key = q/lambda=2.177^circ.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="$\lambda = 2.177^\circ.$">|; 

$key = q/muequivZYB;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$\mu\equiv ZYB$">|; 

$key = q/bar{D}_0=297.864^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1628.png"
 ALT="$\bar{D}_0 = 297.864^\circ$">|; 

$key = q/94.072;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1537.png"
 ALT="$94.072$">|; 

$key = q/{{bf{P};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1640.png"
 ALT="${\bf P}$">|; 

$key = q/C';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1649.png"
 ALT="$C'$">|; 

$key = q/45.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1037.png"
 ALT="$45.0'$">|; 

$key = q/tanL,tandelta<-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$\tan L \tan\delta &lt; -1$">|; 

$key = q/05.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1051.png"
 ALT="$05.6'$">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.00016-1.01131)slash0.02349simeq-0.48.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="419" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1908.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.00016-1.01131)/0.02349 \simeq -0.48.
\end{displaymath}">|; 

$key = q/displaystylesinepsilon,sinlambda,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \sin\epsilon \sin\lambda,$">|; 

$key = q/x=x';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="$x=x'$">|; 

$key = q/PSPi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$P S \Pi$">|; 

$key = q/40.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="$40.0'$">|; 

$key = q/596.791;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1963.png"
 ALT="$596.791$">|; 

$key = q/02.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img967.png"
 ALT="$02.8'$">|; 

$key = q/t-t_0=1,950.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1739.png"
 ALT="$t-t_0=1 950.5$">|; 

$key = q/3.8246times10^{-5},,^circslash{rmday};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="$3.8246\times 10^{-5}  ^\circ/{\rm day}$">|; 

$key = q/359.529;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1924.png"
 ALT="$359.529$">|; 

$key = q/displaystyle1-2,e,cosM+2,e^2,sin^2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="$\displaystyle 1 -2 e \cos M + 2 e^2 \sin^2 M,$">|; 

$key = q/+05^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="$+05^\circ$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{149^circ13'{&{349^circ38'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="973" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $149^\circ 13'$&amp; $349^\circ 38'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/45.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1055.png"
 ALT="$45.6'$">|; 

$key = q/deltabeta_3(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1636.png"
 ALT="$\delta\beta_3(')$">|; 

$key = q/31.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img940.png"
 ALT="$31.8'$">|; 

$key = q/DeltaM_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1468.png"
 ALT="$\Delta M_S$">|; 

$key = q/A=cos^{-1}[sin(338^circ),sin(23^circ26')slashcos(60^circ)]=107^circ20';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$A= \cos^{-1}[\sin (338^\circ) \sin (23^\circ 26')/\cos (60^\circ)] = 107^\circ 20'$">|; 

$key = q/46.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1079.png"
 ALT="$46.4'$">|; 

$key = q/displaystyledeltatheta_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1706.png"
 ALT="$\displaystyle \delta\theta_-$">|; 

$key = q/delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\delta$">|; 

$key = q/^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$^\circ$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{097^circ20'{&{041^circ31'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="973" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $097^\circ 20'$&amp; $041^\circ 31'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/displaystylezeta';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1670.png"
 ALT="$\displaystyle \zeta'$">|; 

$key = q/26.6^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2003.png"
 ALT="$26.6^\circ$">|; 

$key = q/{displaymath}beta=h,beta_0=1.188times1.297=1.541simeq1^circ32'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2081.png"
 ALT="\begin{displaymath}
\beta = h \beta_0 = 1.188\times 1.297 = 1.541 \simeq 1^\circ 32'.
\end{displaymath}">|; 

$key = q/36.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1090.png"
 ALT="$36.8'$">|; 

$key = q/zeta=-0.00953;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1341.png"
 ALT="$\zeta =- 0.00953$">|; 

$key = q/+00^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="$+00^\circ$">|; 

$key = q/{displaymath}bar{mu}=cos^{-1}(-bar{a}).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1949.png"
 ALT="\begin{displaymath}
\bar{\mu} = \cos^{-1}(-\bar{a}).
\end{displaymath}">|; 

$key = q/-175.150;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1531.png"
 ALT="$-175.150$">|; 

$key = q/tilde{n}(^circslash{{rm{day});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1418.png"
 ALT="$\tilde{n}(^\circ/{\rm day})$">|; 

$key = q/{displaymath}beta=h,beta_0=-1.215times2.511=-3.051simeq-3^circ03'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2141.png"
 ALT="\begin{displaymath}
\beta = h \beta_0 =- 1.215\times 2.511 = -3.051\simeq -3^\circ 03'.
\end{displaymath}">|; 

$key = q/v=r',sini,sinF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2100.png"
 ALT="$v= r' \sin i \sin F$">|; 

$key = q/+0^circ20';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$+0^\circ 20'$">|; 

$key = q/zeta_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1699.png"
 ALT="$\zeta_S$">|; 

$key = q/45.4^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1988.png"
 ALT="$45.4^\circ$">|; 

$key = q/+55';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1369.png"
 ALT="$+55'$">|; 

$key = q/Deltabar{D}=bar{D}-bar{D}_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1624.png"
 ALT="$\Delta \bar{D}= \bar{D}-\bar{D}_0$">|; 

$key = q/+86^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="$+86^\circ 34'$">|; 

$key = q/00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="$00'$">|; 

$key = q/R';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$R'$">|; 

$key = q/6.9190;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2145.png"
 ALT="$6.9190$">|; 

$key = q/-132.800;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1525.png"
 ALT="$-132.800$">|; 

$key = q/displaystyle-(1slash2),e^2+[e-(3slash8),e^3],cos,M+(1slash2),e^2,cos,2M+(3slash8),e^3,cos,3M.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="536" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1888.png"
 ALT="$\displaystyle -(1/2) e^2+ [e-(3/8) e^3] \cos M + (1/2) e^2 \cos 2M + (3/8) e^3 \cos 3M.$">|; 

$key = q/R=6371;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1332.png"
 ALT="$R=6371$">|; 

$key = q/{displaymath}z=frac{1-zeta}{1-zeta'},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1667.png"
 ALT="\begin{displaymath}
z = \frac{1-\zeta}{1-\zeta'},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashfig3.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/fig3.eps}}
\end{figure}">|; 

$key = q/+65^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="$+65^\circ 00'$">|; 

$key = q/0.3';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2040.png"
 ALT="$0.3'$">|; 

$key = q/39.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1168.png"
 ALT="$39.4'$">|; 

$key = q/displaystyle-sinL,cosalpha_0,{{bf{v}+(cosL,sinepsilon-sinL,cosepsilon,sinalpha_0),{{bf{s}+(cosL,cosepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="493" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle -\sin L \cos \alpha_0 {\bf v} + (\cos L \sin \epsilon-\sin L \cos \epsilon \sin \alpha_0) {\bf s} + (\cos L \cos \epsilon$">|; 

$key = q/Theta_-(xi)=-Theta_+(-xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1737.png"
 ALT="$\Theta_-(\xi)=-\Theta_+(-\xi)$">|; 

$key = q/{displaymath}a_3=bar{D}simeq358^circ,~~~a_4=M_Ssimeq163^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1510.png"
 ALT="\begin{displaymath}
a_3=\bar{D}\simeq 358^\circ,&nbsp;&nbsp;&nbsp;a_4 = M_S\simeq 163^\circ,
\end{displaymath}">|; 

$key = q/delta(a)=deltaa_0,cosa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1336.png"
 ALT="$\delta(a)=\delta a_0 \cos a$">|; 

$key = q/35^circ38'+105^circ00'=143^circ38';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$35^\circ 38' + 105^\circ00'=
143^\circ 38'$">|; 

$key = q/beta_{Mt}(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1610.png"
 ALT="$\beta_{Mt}(')$">|; 

$key = q/357.588;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="$357.588$">|; 

$key = q/49.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1175.png"
 ALT="$49.6'$">|; 

$key = q/q_2=-1.320^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1570.png"
 ALT="$q_2=-1.320^\circ$">|; 

$key = q/displaystyle-0.051,e,sinM_S,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1206.png"
 ALT="$\displaystyle -0.051 e \sin M_S,$">|; 

$key = q/displaystyle{{bf{s}times{{bf{n}cdot{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$\displaystyle {\bf s}\times {\bf n}\cdot{\bf r}$">|; 

$key = q/{displaymath}r,cosT=a,(cosE-e).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="\begin{displaymath}
r \cos T = a (\cos E - e).
\end{displaymath}">|; 

$key = q/QQ';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$QQ'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere6.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere6.eps}}
\end{figure}">|; 

$key = q/q_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1213.png"
 ALT="$q_i$">|; 

$key = q/displaystyledeltabeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1355.png"
 ALT="$\displaystyle \delta\beta$">|; 

$key = q/18^circ07';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$18^\circ 07'$">|; 

$key = q/{displaymath}alpha=tan^{-1}(tanlambda,cosepsilon)-sin^{-1}left[frac{sinlambda,si}{(1-sin^2lambda,sin^2epsilon)^{1slash2}}right].{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="\begin{displaymath}
\alpha = \tan^{-1}(\tan \lambda \cos \epsilon) - \sin^{-1}\...
...ilon \tan L}{(1-\sin^2\lambda \sin^2\epsilon)^{1/2}}\right].
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashaltitude2.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="337" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/altitude2.eps}}
\end{figure}">|; 

$key = q/-176.102;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1520.png"
 ALT="$-176.102$">|; 

$key = q/3';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1720.png"
 ALT="$3'$">|; 

$key = q/displaystylecosmu=frac{partial{{bf{r}}{partiallambda}cdotfrac{partial{{bf{r}}{partiala};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$\displaystyle \cos \mu = \frac{\partial{\bf r}}{\partial\lambda}\cdot\frac{\partial {\bf r}}{\partial a}$">|; 

$key = q/27.5^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2000.png"
 ALT="$27.5^\circ$">|; 

$key = q/248.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1978.png"
 ALT="$248.3^\circ$">|; 

$key = q/t_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="$t_0$">|; 

$key = q/-08^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="$-08^\circ 26'$">|; 

$key = q/2bar{F};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1437.png"
 ALT="$2\bar{F}$">|; 

$key = q/{displaymath}alpha_0=alpha-90^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="\begin{displaymath}
\alpha_0 = \alpha-90^\circ,
\end{displaymath}">|; 

$key = q/displaystyle{{rm{Area},PiPS;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="$\displaystyle {\rm Area}  \Pi PS$">|; 

$key = q/60';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="$60'$">|; 

$key = q/10.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="$10.2'$">|; 

$key = q/+1.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="$+1.0$">|; 

$key = q/-03^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="$-03^\circ 26'$">|; 

$key = q/240^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$240^\circ$">|; 

$key = q/42.961;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="$42.961$">|; 

$key = q/alpha_0=0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\alpha_0 = 0^\circ$">|; 

$key = q/12.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img944.png"
 ALT="$12.0'$">|; 

$key = q/47.0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1986.png"
 ALT="$47.0^\circ$">|; 

$key = q/1^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$1^\circ$">|; 

$key = q/17.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1112.png"
 ALT="$17.6'$">|; 

$key = q/z=z_{{rm{min};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1685.png"
 ALT="$z=z_{\rm min}$">|; 

$key = q/0.03350830;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="$0.03350830$">|; 

$key = q/180^circ-sin^{-1}(cosLslashsinepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$180^\circ -
\sin^{-1}(\cos L/\sin \epsilon)$">|; 

$key = q/269.350;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1237.png"
 ALT="$269.350$">|; 

$key = q/-446.741;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="$-446.741$">|; 

$key = q/deltatheta_{pm}(360^circ-mu)=-deltatheta_{pm}(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1868.png"
 ALT="$\delta\theta_{\pm}(360^\circ-\mu) = -\delta\theta_{\pm}(\mu)$">|; 

$key = q/233^circ09';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$233^\circ 09'$">|; 

$key = q/bar{z}=1.00016;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1906.png"
 ALT="$\bar{z}= 1.00016$">|; 

$key = q/697.132;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1252.png"
 ALT="$697.132$">|; 

$key = q/L;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$L$">|; 

$key = q/PZ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="$PZ$">|; 

$key = q/sina=cosL,cosalpha_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$\sin a = \cos L \cos \alpha_0$">|; 

$key = q/cosA={{bf{r}cdot{{bf{n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$\cos A = {\bf r}\cdot {\bf n}$">|; 

$key = q/0.093394;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="$0.093394$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{139^circ00'{&{359^circ51'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="973" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $139^\circ 00'$&amp; $359^\circ 51'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/SCBE;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$SCBE$">|; 

$key = q/25';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="$25'$">|; 

$key = q/27.9^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1994.png"
 ALT="$27.9^\circ$">|; 

$key = q/{displaymath}q(120^circ)=1.641^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="\begin{displaymath}
q(120^\circ)= 1.641^\circ,
\end{displaymath}">|; 

$key = q/displaystyle-0.038,e_M,sin2bar{F}_M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1456.png"
 ALT="$\displaystyle -0.038 e_M \sin 2 \bar{F}_M,$">|; 

$key = q/167.083;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="$167.083$">|; 

$key = q/00.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="$00.2'$">|; 

$key = q/{displaymath}xi=(bar{z}-z)slashdeltaz=(1.00184-1.02244)slash0.11014simeq-0.19.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="419" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1783.png"
 ALT="\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.00184-1.02244)/0.11014 \simeq -0.19.
\end{displaymath}">|; 

$key = q/12^h53^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="$12^h53^m$">|; 

$key = q/247.938;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2061.png"
 ALT="$247.938$">|; 

$key = q/45.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1061.png"
 ALT="$45.8'$">|; 

$key = q/+83^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="$+83^\circ 26'$">|; 

$key = q/{displaymath}M=E-e,sinE,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="\begin{displaymath}
M = E - e \sin E,
\end{displaymath}">|; 

$key = q/163.229;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1507.png"
 ALT="$163.229$">|; 

$key = q/164.071;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1742.png"
 ALT="$164.071$">|; 

$key = q/07.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1111.png"
 ALT="$07.6'$">|; 

$key = q/{displaymath}sina=cosL,coslambda,sinalpha+sinL,sinepsilon,sinlambda-cosL,cosepsilon,sinlambda,cosalpha,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="\begin{displaymath}
\sin a= \cos L \cos\lambda \sin\alpha + \sin L \sin\epsilon \sin\lambda - \cos L \cos\epsilon \sin\lambda \cos\alpha,
\end{displaymath}">|; 

$key = q/deltabeta_1(');MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1634.png"
 ALT="$\delta\beta_1(')$">|; 

$key = q/M_0=49.237^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1981.png"
 ALT="$M_0 = 49.237^\circ$">|; 

$key = q/deltabeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1351.png"
 ALT="$\delta\beta$">|; 

$key = q/11.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img932.png"
 ALT="$11.6'$">|; 

$key = q/~+2^circ04';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="$&nbsp;+2^\circ 04'$">|; 

$key = q/174.693;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="$174.693$">|; 

$key = q/{displaymath}left(frac{t-t_ast}{tau}right)pi,a,b=frac{1}{2},r^2,cosT,sinT+frac{b}{a},frac{a^2}{2},(E-cosE,sinE).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="\begin{displaymath}
\left(\frac{t-t_\ast}{\tau}\right) \pi a b= \frac{1}{2} r...
... T \sin T + \frac{b}{a} \frac{a^2}{2} (E - \cos E \sin E).
\end{displaymath}">|; 

$key = q/displaystyletheta(mu,bar{z}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1688.png"
 ALT="$\displaystyle \theta(\mu,\bar{z}),$">|; 

$key = q/6^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1361.png"
 ALT="$6^\circ$">|; 

$key = q/bar{theta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1724.png"
 ALT="$\bar{\theta}$">|; 

$key = q/displaystylea,sini,sinF,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2106.png"
 ALT="$\displaystyle a \sin i \sin F,$">|; 

$key = q/35.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1048.png"
 ALT="$35.4'$">|; 

$key = q/93.284;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1249.png"
 ALT="$93.284$">|; 

$key = q/displaystyle-sinalpha_0,{{bf{v}+cosalpha_0,{{bf{u},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle -\sin \alpha_0 {\bf v} + \cos \alpha_0 {\bf u},$">|; 

$key = q/+4.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1406.png"
 ALT="$+4.00$">|; 

$key = q/04.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1003.png"
 ALT="$04.0'$">|; 

$key = q/displaystyleTheta_+(xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1695.png"
 ALT="$\displaystyle \Theta_+(\xi)$">|; 

$key = q/-7^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="$-7^\circ 00'$">|; 

$key = q/displaystyleq_3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1203.png"
 ALT="$\displaystyle q_3$">|; 

$key = q/{displaymath}h=Theta_-,deltah_-+bar{h}+Theta_+,deltah_+=-0.355times0.008+0.591-0.125times0.008=0.587.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2124.png"
 ALT="\begin{displaymath}
h = \Theta_- \delta h_- + \bar{h}+\Theta_+ \delta h_+ = -0.355\times 0.008+0.591-0.125\times 0.008 = 0.587.
\end{displaymath}">|; 

$key = q/05^circ18';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$05^\circ 18'$">|; 

$key = q/{displaymath}beta_0(96^circ)=1.297^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2077.png"
 ALT="\begin{displaymath}
\beta_0(96^\circ) = 1.297^\circ.
\end{displaymath}">|; 

$key = q/-328.042;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1768.png"
 ALT="$-328.042$">|; 

$key = q/nomath_inline{dagnomath_inline{;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="$\dag $">|; 

$key = q/43.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img983.png"
 ALT="$43.2'$">|; 

$key = q/43.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img977.png"
 ALT="$43.0'$">|; 

$key = q/F=bar{F}+q_1+q_2+q_3+q_4+q_5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1314.png"
 ALT="$F = \bar{F}+q_1+q_2+q_3+q_4+q_5$">|; 

$key = q/12.37times0.185simeq2.3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1618.png"
 ALT="$12.37\times 0.185\simeq 2.3$">|; 

$key = q/-605.953;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1283.png"
 ALT="$-605.953$">|; 

$key = q/A;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$A$">|; 

$key = q/mu=188.649^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1798.png"
 ALT="$\mu=188.649^\circ$">|; 

$key = q/{displaymath}deltah_-(253^circ)=0.184,mbox{hspace{0.5cm}}bar{h}(253^circ)=1.037,mbox{hspace{0.5cm}}deltah_+(253^circ)=0.272,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="463" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2139.png"
 ALT="\begin{displaymath}
\delta h_-(253^\circ) = 0.184,\mbox{\hspace{0.5cm}}\bar{h}(2...
...rc)=1.037, \mbox{\hspace{0.5cm}}\delta h_+(253^\circ) = 0.272,
\end{displaymath}">|; 

$key = q/-1.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1386.png"
 ALT="$-1.00$">|; 

$key = q/XR';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$XR'$">|; 

$key = q/{displaymath}frac{RP}{RQ}=frac{b}{a}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img636.png"
 ALT="\begin{displaymath}
\frac{RP}{RQ} = \frac{b}{a}.
\end{displaymath}">|; 

$key = q/1.3044;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2151.png"
 ALT="$1.3044$">|; 

$key = q/{displaymath}a_{{rm{-}=|L+delta|-90^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{displaymath}
a_{\rm -} = \vert L+\delta\vert - 90^\circ.
\end{displaymath}">|; 

$key = q/16.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1082.png"
 ALT="$16.6'$">|; 

$key = q/-149.506;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1268.png"
 ALT="$-149.506$">|; 

$key = q/Msimeq230^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1926.png"
 ALT="$M\simeq 230^\circ$">|; 

$key = q/26.201;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1747.png"
 ALT="$26.201$">|; 

$key = q/Deltabar{D}(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1620.png"
 ALT="$\Delta \bar{D}(^\circ)$">|; 

$key = q/bar{a}=aslashbar{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1946.png"
 ALT="$\bar{a}=a/\bar{z}$">|; 

$key = q/{displaymath}frac{{{rm{Area},PiPS}{pi,a,b}=frac{t-t_ast}{tau},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="\begin{displaymath}
\frac{{\rm Area} \Pi PS}{\pi a b} = \frac{t-t_\ast}{\tau},
\end{displaymath}">|; 

$key = q/360^circ-lambda_c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$360^\circ-\lambda_c$">|; 

$key = q/-28';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1401.png"
 ALT="$-28'$">|; 

$key = q/displaystyledeltah_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2032.png"
 ALT="$\displaystyle \delta h_-$">|; 

$key = q/n;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$n$">|; 

$key = q/q_3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1439.png"
 ALT="$q_3$">|; 

$key = q/Theta_-=0.101;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2054.png"
 ALT="$\Theta_-=0.101$">|; 

$key = q/a_1=M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1223.png"
 ALT="$a_1=M$">|; 

$key = q/Deltabar{lambda};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="$\Delta\bar{\lambda}$">|; 

$key = q/R_E;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1558.png"
 ALT="$R_E$">|; 

$key = q/23^circ13';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$23^\circ 13'$">|; 

$key = q/181.973;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="$181.973$">|; 

$key = q/DeltaM_S(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1622.png"
 ALT="$\Delta M_S(^\circ)$">|; 

$key = q/NG'N';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2099.png"
 ALT="$NG'N'$">|; 

$key = q/{displaymath}alpha=sin^{-1}(tanlambda,cosepsilon).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="\begin{displaymath}
\alpha = \sin ^{-1}(\tan \lambda \cos\epsilon).
\end{displaymath}">|; 

$key = q/-366.186;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="$-366.186$">|; 

$key = q/+3.3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="$+3.3$">|; 

$key = q/q=2.561^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2083.png"
 ALT="$q= 2.561^\circ$">|; 

$key = q/12^circ23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$12^\circ 23'$">|; 

$key = q/n,(^circslash{{rm{day});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="$n (^\circ/{\rm day})$">|; 

$key = q/+36^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="$+36^\circ 34'$">|; 

$key = q/03';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="$03'$">|; 

$key = q/39.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1156.png"
 ALT="$39.0'$">|; 

$key = q/1.60213040;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="$1.60213040$">|; 

$key = q/55';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="$55'$">|; 

$key = q/{displaymath}sina=cosL,cos(alpha-alpha_0)=cosL,sin(alpha_0-alpha+90^circ).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="\begin{displaymath}
\sin a = \cos L \cos(\alpha - \alpha_0) = \cos L \sin (\alpha_0-\alpha + 90^\circ).
\end{displaymath}">|; 

$key = q/{displaymath}tsimeqt_0+(360-261.515)slash0.61652137simeqt_0+160,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1936.png"
 ALT="\begin{displaymath}
t\simeq t_0 + (360-261.515)/0.61652137\simeq
t_0 + 160  {\rm JD}.
\end{displaymath}">|; 

$key = q/displaystylea,(1-e,cosT-e^2,sin^2T),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$\displaystyle a (1-e \cos T - e^2 \sin^2 T),$">|; 

$key = q/bar{mu}=136.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1950.png"
 ALT="$\bar{\mu} = 136.3^\circ$">|; 

$key = q/PiQDA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="$\Pi QDA$">|; 

$key = q/+85^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$+85^\circ $">|; 

$key = q/displaystyletheta(mu,bar{z})-theta(mu,z_{{rm{max}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1690.png"
 ALT="$\displaystyle \theta(\mu,\bar{z}) - \theta(\mu,z_{\rm max}),$">|; 

$key = q/37';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="$37'$">|; 

$key = q/beta_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2044.png"
 ALT="$\beta_0$">|; 

$key = q/{displaymath}deltatheta_-(287^circ)=-0.353^circ,mbox{hspace{0.5cm}}bar{theta}(28space{0.5cm}}deltatheta_+(287^circ)=-0.405^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1853.png"
 ALT="\begin{displaymath}
\delta\theta_-(287^\circ) = -0.353^\circ,\mbox{\hspace{0.5cm...
...\mbox{\hspace{0.5cm}}\delta\theta_+(287^\circ) = -0.405^\circ.
\end{displaymath}">|; 

$key = q/|L+delta|>90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$\vert L+\delta\vert&gt; 90^\circ$">|; 

$key = q/a_5=2bar{F}_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1473.png"
 ALT="$a_5=2\bar{F}_M$">|; 

$key = q/displaystylebar{lambda}_M-bar{lambda}_S,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1451.png"
 ALT="$\displaystyle \bar{\lambda}_M - \bar{\lambda}_S,$">|; 

$key = q/65.273;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1533.png"
 ALT="$65.273$">|; 

$key = q/-3.8246times10^{-5},,^circslash{{rm{day};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="$-3.8246\times 10^{-5}  ^\circ/{\rm day}$">|; 

$key = q/8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$8'$">|; 

$key = q/293.660;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2073.png"
 ALT="$293.660$">|; 

$key = q/427.003;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1898.png"
 ALT="$427.003$">|; 

$key = q/pi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$\pi$">|; 

$key = q/840.001;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="$840.001$">|; 

$key = q/{displaymath}cosA=frac{sinlambda,sinepsilon}{cosL}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="\begin{displaymath}
\cos A = \frac{\sin\lambda \sin\epsilon}{\cos L}.
\end{displaymath}">|; 

$key = q/261.300;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1491.png"
 ALT="$261.300$">|; 

$key = q/sina_{{rm{-}=-cos(L+delta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\sin a_{\rm -} =- \cos (L+\delta)$">|; 

$key = q/90^circ-|L-epsilon|;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$90^\circ - \vert L- \epsilon\vert$">|; 

$key = q/{displaymath}|beta_{syz}|<delta_M+rho_S-rho_M,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1585.png"
 ALT="\begin{displaymath}
\vert\beta_{syz}\vert &lt; \delta_M + \rho_S-\rho_M,
\end{displaymath}">|; 

$key = q/XP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$XP$">|; 

$key = q/45';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="$45'$">|; 

$key = q/{displaymath}Theta_-(-0.59)=-0.469,mbox{hspace{0.5cm}}Theta_+(-0.59)=-0.121,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1835.png"
 ALT="\begin{displaymath}
\Theta_-(-0.59) = -0.469, \mbox{\hspace{0.5cm}}\Theta_+(-0.59) = -0.121,
\end{displaymath}">|; 

$key = q/NGG';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2012.png"
 ALT="$NGG'$">|; 

$key = q/-5.914;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1529.png"
 ALT="$-5.914$">|; 

$key = q/DeltaM=M-M_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1186.png"
 ALT="$\Delta M = M - M_0$">|; 

$key = q/27.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1119.png"
 ALT="$27.8'$">|; 

$key = q/27.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1107.png"
 ALT="$27.4'$">|; 

$key = q/08^circ52';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="$08^\circ 52'$">|; 

$key = q/deltabeta_2=rho_{M,0},e_M,cosM_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1590.png"
 ALT="$\delta\beta_2= \rho_{M 0} e_M \cos M_M$">|; 

$key = q/23.163;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1849.png"
 ALT="$23.163$">|; 

$key = q/rho_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2161.png"
 ALT="$\rho_M$">|; 

$key = q/q_5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1220.png"
 ALT="$q_5$">|; 

$key = q/+01^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="$+01^\circ 34'$">|; 

$key = q/-209.986;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1271.png"
 ALT="$-209.986$">|; 

$key = q/lambda=240^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$\lambda=240^\circ$">|; 

$key = q/-72.793;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1270.png"
 ALT="$-72.793$">|; 

$key = q/displaystyle-(1slash2),xi,(xi-1),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1694.png"
 ALT="$\displaystyle - (1/2) \xi (\xi-1),$">|; 

$key = q/{displaymath}z=(1-zeta_S)slash(1-zeta)=(1+8.56times10^{-3})slash(1+1.367times10^{-1})=0.8873.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1970.png"
 ALT="\begin{displaymath}
z= (1-\zeta_S)/(1-\zeta) = (1+8.56\times 10^{-3})/(1+1.367\times 10^{-1}) =
0.8873.
\end{displaymath}">|; 

$key = q/21.1^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2002.png"
 ALT="$21.1^\circ$">|; 

$key = q/PiPBA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$\Pi PBA$">|; 

$key = q/rho;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="$\rho$">|; 

$key = q/{displaymath}tsimeqt_0+(540-284.998)slash0.46157617simeqt_0+552,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1797.png"
 ALT="\begin{displaymath}
t\simeq t_0+(540-284.998)/0.46157617\simeq t_0 + 552  {\rm JD}.
\end{displaymath}">|; 

$key = q/49.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1157.png"
 ALT="$49.0'$">|; 

$key = q/+1^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$+1^\circ 00'$">|; 

$key = q/196.501;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1825.png"
 ALT="$196.501$">|; 

$key = q/32.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img946.png"
 ALT="$32.0'$">|; 

$key = q/-10^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$-10^\circ$">|; 

$key = q/{displaymath}lambda=25.950simeq25^circ57'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img1295.png"
 ALT="\begin{displaymath}
\lambda =25.950\simeq 25^\circ 57'.
\end{displaymath}">|; 

$key = q/+8^circ38';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$+8^\circ 38'$">|; 

$key = q/0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$0$">|; 

$key = q/{displaymath}mu=bar{lambda}+q-bar{lambda}_S=359.529-0.592-273.055=85.882simeq86^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1928.png"
 ALT="\begin{displaymath}
\mu=\bar{\lambda}+q-\bar{\lambda}_S =359.529-0.592-273.055= 85.882\simeq 86^\circ.
\end{displaymath}">|; 

$key = q/15.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1040.png"
 ALT="$15.2'$">|; 

$key = q/{displaymath}theta(mu,z)simeqTheta_-(xi),deltatheta_-(mu)+bar{theta}(mu)+Theta_+(xi),deltatheta_+(mu),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1686.png"
 ALT="\begin{displaymath}
\theta(\mu,z)\simeq \Theta_-(\xi) \delta\theta_-(\mu) + \bar{\theta}(\mu)
+ \Theta_+(\xi) \delta\theta_+(\mu),
\end{displaymath}">|; 

$key = q/GR';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$GR'$">|; 

$key = q/CQP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="$CQP$">|; 

$key = q/deltalambda;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1350.png"
 ALT="$\delta\lambda$">|; 

$key = q/+3.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$+3.0$">|; 

$key = q/bar{mu}=163.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1814.png"
 ALT="$\bar{\mu}=163.3^\circ$">|; 

$key = q/displaystylefrac{partial{{bf{r}}{partiala};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$\displaystyle \frac{\partial {\bf r}}{\partial a}$">|; 

$key = q/105^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$105^\circ$">|; 

$key = q/displaystylebeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2038.png"
 ALT="$\displaystyle \beta$">|; 

$key = q/bar{lambda}';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1660.png"
 ALT="$\bar{\lambda}'$">|; 

$key = q/04^circ50';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$04^\circ 50'$">|; 

$key = q/+21^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="$+21^\circ 34'$">|; 

$key = q/13^h33^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="$13^h33^m$">|; 

$key = q/displaystyletanA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle \tan A$">|; 

$key = q/32.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img964.png"
 ALT="$32.6'$">|; 

$key = q/11^circ27';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="$11^\circ 27'$">|; 

$key = q/{{bf{P}';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1642.png"
 ALT="${\bf P}'$">|; 

$key = q/4.09233439;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="$4.09233439$">|; 

$key = q/{figure}{epsfysize{=5.5in{centerline{epsffile{epsfilesslashecliptic2.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="753" HEIGHT="517" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="\begin{figure}
\epsfysize =5.5in
\centerline{\epsffile{epsfiles/ecliptic2.eps}}
\end{figure}">|; 

$key = q/P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$P$">|; 

$key = q/18.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1136.png"
 ALT="$18.4'$">|; 

$key = q/e^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$e^2$">|; 

$key = q/i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1214.png"
 ALT="$i$">|; 

$key = q/mu=21.689^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2113.png"
 ALT="$\mu= 21.689^\circ$">|; 

$key = q/+2.6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$+2.6$">|; 

$key = q/19.3^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1998.png"
 ALT="$19.3^\circ$">|; 

$key = q/{displaymath}q(237^circ)=-16.974^circ,mbox{hspace{0.5cm}}zeta(237^circ)=-1.367times10^{-1},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1967.png"
 ALT="\begin{displaymath}
q(237^\circ)= -16.974^\circ, \mbox{\hspace{0.5cm}}\zeta(237^\circ)=-1.367\times 10^{-1},
\end{displaymath}">|; 

$key = q/+3.6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$+3.6$">|; 

$key = q/{displaymath}a_3=bar{D}simeq185^circ,~~~a_4=M_Ssimeq65^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1539.png"
 ALT="\begin{displaymath}
a_3=\bar{D}\simeq 185^\circ,&nbsp;&nbsp;&nbsp;a_4 = M_S\simeq 65^\circ,
\end{displaymath}">|; 

$key = q/0.98560025;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="$0.98560025$">|; 

$key = q/6.5%;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1616.png"
 ALT="$6.5\%$">|; 

$key = q/M_{M,0}=134.916^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1631.png"
 ALT="$M_{M 0} = 134.916^\circ$">|; 

$key = q/displaystyle{{bf{s}times{{bf{e}cdot{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$\displaystyle {\bf s}\times {\bf e}\cdot{\bf r}$">|; 

$key = q/-105.876;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1276.png"
 ALT="$-105.876$">|; 

$key = q/{displaymath}q_1(a_1)=0.101^circ,~~q_2(a_2)=0.070^circ,~~q_3(a_3)=-0.045^circ,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1512.png"
 ALT="\begin{displaymath}
q_1(a_1)=0.101^\circ,&nbsp;&nbsp;q_2(a_2)= 0.070^\circ,&nbsp;&nbsp;q_3(a_3) = -0.045^\circ,
\end{displaymath}">|; 

$key = q/SL=rho-2,e,a,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$SL = \rho-2 e a \cos M$">|; 

$key = q/51.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img918.png"
 ALT="$51.0'$">|; 

$key = q/T;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="$T$">|; 

$key = q/{displaymath}sinq=frac{WP}{SP}=frac{2,e,sinM}{(1-2,e,cosM+e^2+3,e^2,sin^2M)^{1slash2}}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="\begin{displaymath}
\sin q = \frac{WP}{SP} = \frac{2 e \sin M}{(1-2 e \cos M +e^2+3 e^2 \sin^2 M)^{1/2}}.
\end{displaymath}">|; 

$key = q/SS';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$SS'$">|; 

$key = q/{displaymath}beta_0(241^circ)=-1.615^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2063.png"
 ALT="\begin{displaymath}
\beta_0(241^\circ) = -1.615^\circ.
\end{displaymath}">|; 

$key = q/50.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="$50.2'$">|; 

$key = q/46.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1085.png"
 ALT="$46.6'$">|; 

$key = q/{displaymath}bar{lambda}=varpi+M,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="\begin{displaymath}
\bar{\lambda} = \varpi + M,
\end{displaymath}">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00}{}multicolumn{4}{c}{}multicolumn{4}{c}{}tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="858" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...
\multicolumn{4}{c}{}\\\\
\multicolumn{4}{c}{}\\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/360slash0.61652137=583.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1942.png"
 ALT="$360/0.61652137= 583.9$">|; 

$key = q/38';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="$38'$">|; 

$key = q/44.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1025.png"
 ALT="$44.6'$">|; 

$key = q/requivGG';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1664.png"
 ALT="$r\equiv GG'$">|; 

$key = q/{displaymath}beta_{Mt}=25.41'+deltabeta_1(M_M)-deltabeta_2(M_M)-deltabeta_3(M_S).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1588.png"
 ALT="\begin{displaymath}
\beta_{Mt} = 25.41' + \delta\beta_1(M_M)-\delta\beta_2 (M_M)-\delta\beta_3(M_S).
\end{displaymath}">|; 

$key = q/21.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img921.png"
 ALT="$21.2'$">|; 

$key = q/L=-23^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$L=-23^\circ 26'$">|; 

$key = q/{Parallel}{}{}ParallelLText{{{small{tabular{{l|lll}multicolumn{4}{c}{Aries}00:00&{00^circ00'{&{085^circ55'{&{052^circ56'{tabular{}}{Parallel};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="878" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="\begin{Parallel}{}{}
\ParallelLText{
{\small
\begin{tabular}{l\vert lll}
\multi...
...irc 00'$ &amp; $085^\circ 55'$&amp; $052^\circ 56'$ \\\\
\end{tabular}}}
\end{Parallel}">|; 

$key = q/M_{S,0}=357.588^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1630.png"
 ALT="$M_{S 0} = 357.588^\circ$">|; 

$key = q/displaystyle{{bf{u};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle {\bf u}$">|; 

$key = q/{displaymath}bar{theta}=tan^{-1}left(frac{sinbar{mu}}{bar{a}+cosbar{mu}}right),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1807.png"
 ALT="\begin{displaymath}
\bar{\theta} = \tan^{-1}\left(\frac{\sin \bar{\mu}}{\bar{a}+\cos\bar{\mu}}\right),
\end{displaymath}">|; 

$key = q/DeltaM_S=M_S-M_{S,0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1626.png"
 ALT="$\Delta M_S = M_S - M_{S 0}$">|; 

$key = q/46.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1073.png"
 ALT="$46.2'$">|; 

$key = q/{displaymath}lambda=bar{lambda}_S+theta=44.602-25.642=18.960simeq18^circ58'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1976.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda}_S + \theta= 44.602-25.642=18.960 \simeq 18^\circ 58'.
\end{displaymath}">|; 

$key = q/+2^circ46';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="$+2^\circ 46'$">|; 

$key = q/{displaymath}h=Theta_-,deltah_-+bar{h}+Theta_+,deltah_+=-0.101times0.017+1.056-0.619times0.027=1.038.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2066.png"
 ALT="\begin{displaymath}
h = \Theta_- \delta h_- + \bar{h}+\Theta_+ \delta h_+ = -0.101\times 0.017+1.056-0.619\times 0.027 = 1.038.
\end{displaymath}">|; 

$key = q/14^h51m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="$14^h51m$">|; 

$key = q/{displaymath}deltah_-(22^circ)=0.008,mbox{hspace{0.5cm}}bar{h}(22^circ)=0.591,mbox{hspace{0.5cm}}deltah_+(22^circ)=0.008,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2123.png"
 ALT="\begin{displaymath}
\delta h_-(22^\circ) = 0.008,\mbox{\hspace{0.5cm}}\bar{h}(22^\circ)=0.591, \mbox{\hspace{0.5cm}}\delta h_+(22^\circ) = 0.008,
\end{displaymath}">|; 

$key = q/+35^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="$+35^\circ 00'$">|; 

$key = q/15.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1034.png"
 ALT="$15.0'$">|; 

$key = q/10.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="$10.8'$">|; 

$key = q/83.108;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2132.png"
 ALT="$83.108$">|; 

$key = q/XZ=LW=(1slash2),e,a,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="$XZ =LW = (1/2) e a \cos M$">|; 

$key = q/t=2,448,784.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="$t=2 448 784.0$">|; 

$key = q/43^circ19';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1343.png"
 ALT="$43^\circ 19'$">|; 

$key = q/15.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1046.png"
 ALT="$15.4'$">|; 

$key = q/A=180^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$A=180^\circ$">|; 

$key = q/V;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$V$">|; 

$key = q/M_S=353.814^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1266.png"
 ALT="$M_S= 353.814^\circ$">|; 

$key = q/displaystyletanlambda;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle \tan\lambda$">|; 

$key = q/38.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1138.png"
 ALT="$38.4'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere10.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere10.eps}}
\end{figure}">|; 

$key = q/deltabeta_1=delta_{M,0},e_M,cosM_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1589.png"
 ALT="$\delta\beta_1=\delta_{M 0} e_M \cos M_M$">|; 

$key = q/0.387098;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="$0.387098$">|; 

$key = q/NS;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$NS$">|; 

$key = q/SL=a-2,e,a,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="$SL = a-2 e a \cos M$">|; 

$key = q/Arightarrow180^circ-A;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$A\rightarrow180^\circ-A$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere4.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="341" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere4.eps}}
\end{figure}">|; 

$key = q/162.169;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1891.png"
 ALT="$162.169$">|; 

$key = q/+30^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$+30^\circ $">|; 

$key = q/-241.301;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1917.png"
 ALT="$-241.301$">|; 

$key = q/50.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="$50.8'$">|; 

$key = q/mu=-9.583^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1792.png"
 ALT="$\mu=-9.583^\circ$">|; 

$key = q/displaystylecosepsilon,sindelta-sinepsilon,cosdelta,sinalpha,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle \cos\epsilon \sin\delta - \sin\epsilon \cos\delta \sin\alpha,$">|; 

$key = q/{displaymath}sinq=frac{PL}{SP}=frac{2,e,sinM}{(1-4,e,cosM+4,e^2)^{1slash2}}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="\begin{displaymath}
\sin q = \frac{PL}{SP} = \frac{2 e \sin M}{(1-4 e \cos M + 4 e^2)^{1/2}}.
\end{displaymath}">|; 

$key = q/{displaymath}deltatheta_-(86^circ)=0.589^circ,mbox{hspace{0.5cm}}bar{theta}(86^c{hspace{0.5cm}}deltatheta_+(86^circ)=0.607^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="463" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1929.png"
 ALT="\begin{displaymath}
\delta\theta_-(86^\circ) = 0.589^\circ, \mbox{\hspace{0.5cm}...
..., \mbox{\hspace{0.5cm}}\delta\theta_+(86^\circ) = 0.607^\circ.
\end{displaymath}">|; 

$key = q/17^h06^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="$17^h06^m$">|; 

$key = q/-5.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1366.png"
 ALT="$-5.00$">|; 

$key = q/zeta_S(M_S)=-8.56times10^{-3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1741.png"
 ALT="$\zeta_S(M_S)= -8.56\times 10^{-3}$">|; 

$key = q/-4^circ02';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$-4^\circ 02'$">|; 

$key = q/-340.525;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1282.png"
 ALT="$-340.525$">|; 

$key = q/-171.200;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="$-171.200$">|; 

$key = q/-88.704;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="$-88.704$">|; 

$key = q/displaystyle{{rm{Area},PiRQ={{rm{Area},PiQC-{{rm{Area},RQC=frac{1}{2},E,a^2-frac{1}{2},a^2,cosE,sinE.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="509" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="$\displaystyle {\rm Area} \Pi RQ = {\rm Area} \Pi QC - {\rm Area} RQC= \frac{1}{2} E a^2 - \frac{1}{2} a^2 \cos E \sin E.$">|; 

$key = q/rho_U=R_Uslashr_M=delta_M-rho_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1561.png"
 ALT="$\rho_U = R_U/r_M = \delta_M-\rho_S$">|; 

$key = q/bar{lambda}_0=218.322^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1427.png"
 ALT="$\bar{\lambda}_0 = 218.322^\circ$">|; 

$key = q/D=360.00^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1515.png"
 ALT="$D=360.00^\circ$">|; 

$key = q/{displaymath}mu=T'+varpi'-T-varpi=bar{lambda}'+q'-bar{lambda}-q,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1659.png"
 ALT="\begin{displaymath}
\mu =T'+\varpi' - T - \varpi = \bar{\lambda}' + q' - \bar{\lambda}-q,
\end{displaymath}">|; 

$key = q/25.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1059.png"
 ALT="$25.8'$">|; 

$key = q/{displaymath}varpi=varpi_0+varpi_1,(t-t_0).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="\begin{displaymath}
\varpi = \varpi_0 + \varpi_1 (t-t_0).
\end{displaymath}">|; 

$key = q/63.062;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1536.png"
 ALT="$63.062$">|; 

$key = q/displaystylefrac{cosE-e}{1-e,cosE}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="$\displaystyle \frac{\cos E - e}{1-e \cos E}.$">|; 

$key = q/t=2,378,854.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="$t = 2 378 854.5$">|; 

$key = q/-2.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1381.png"
 ALT="$-2.00$">|; 

$key = q/09^circ56';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="$09^\circ 56'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashsphere7.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="338" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/sphere7.eps}}
\end{figure}">|; 

$key = q/27^circ10';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$27^\circ 10'$">|; 

$key = q/03.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img973.png"
 ALT="$03.0'$">|; 

$key = q/{displaymath}theta(mu,z)equivtan^{-1}left[frac{sinmu}{(aslasha'),z+cosmu}right]{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1673.png"
 ALT="\begin{displaymath}
\theta(\mu,z) \equiv \tan^{-1}\left[ \frac{\sin\mu}{(a/a') z+ \cos\mu}\right]
\end{displaymath}">|; 

$key = q/mu=114.5^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1861.png"
 ALT="$\mu=114.5^\circ$">|; 

$key = q/12^h00^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="$12^h00^m$">|; 

$key = q/SPequivr;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="$SP\equiv r$">|; 

$key = q/184.131;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1535.png"
 ALT="$184.131$">|; 

$key = q/162.138;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2116.png"
 ALT="$162.138$">|; 

$key = q/displaystyleh(mu,bar{z})equivleft[1+2,(a,bar{z})^{-1},cosmu+(a,bar{z})^{-2}right]^{-1slash2},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2031.png"
 ALT="$\displaystyle h(\mu,\bar{z})\equiv\left[1 + 2 (a \bar{z})^{-1} \cos\mu+ (a \bar{z})^{-2}\right]^{-1/2},$">|; 

$key = q/lambda=0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\lambda = 0^\circ$">|; 

$key = q/daslashdt>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$da/dt&gt;0$">|; 

$key = q/Theta_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1733.png"
 ALT="$\Theta_-$">|; 

$key = q/37.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1108.png"
 ALT="$37.4'$">|; 

$key = q/Deltabar{F}_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1467.png"
 ALT="$\Delta \bar{F}_M$">|; 

$key = q/36.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1066.png"
 ALT="$36.0'$">|; 

$key = q/14^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$14^\circ 00'$">|; 

$key = q/displaystyle0.211,e_M,(sin2bar{D}-0.066,sinbar{D}),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1454.png"
 ALT="$\displaystyle 0.211 e_M (\sin 2\bar{D} - 0.066 \sin \bar{D}),$">|; 

$key = q/displaystylesinalpha_0,{{bf{u}+cosalpha_0,{{bf{v},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle \sin \alpha_0 {\bf u} + \cos \alpha_0 {\bf v},$">|; 

$key = q/L=-66^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$L=-66^\circ 34'$">|; 

$key = q/4.09237703;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="$4.09237703$">|; 

$key = q/20.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="$20.0'$">|; 

$key = q/L=0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$L=0^\circ$">|; 

$key = q/35.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1036.png"
 ALT="$35.0'$">|; 

$key = q/182^d15^h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="$182^d15^h$">|; 

$key = q/39';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="$39'$">|; 

$key = q/22^circ08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="$22^\circ 08'$">|; 

$key = q/{displaymath}deltatheta_-(202^circ)=-5.980^circ,mbox{hspace{0.5cm}}bar{theta}(20space{0.5cm}}deltatheta_+(202^circ)=-8.955^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="530" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1781.png"
 ALT="\begin{displaymath}
\delta\theta_-(202^\circ) = -5.980^\circ,\mbox{\hspace{0.5cm...
...\mbox{\hspace{0.5cm}}\delta\theta_+(202^\circ) = -8.955^\circ.
\end{displaymath}">|; 

$key = q/114.047;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1286.png"
 ALT="$114.047$">|; 

$key = q/displaystylecosepsilon,tanlambda,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$\displaystyle \cos\epsilon \tan\lambda,$">|; 

$key = q/09.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1177.png"
 ALT="$09.8'$">|; 

$key = q/Msimeq354^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="$M\simeq 354^\circ$">|; 

$key = q/a_3=tilde{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1225.png"
 ALT="$a_3=\tilde{D}$">|; 

$key = q/2e;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$2e$">|; 

$key = q/L=+10^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$L=+10^\circ$">|; 

$key = q/thetaequivPGG';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1662.png"
 ALT="$\theta\equiv PGG'$">|; 

$key = q/50.059;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="$50.059$">|; 

$key = q/-08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1385.png"
 ALT="$-08'$">|; 

$key = q/30.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="$30.8'$">|; 

$key = q/M_S=120.001^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1233.png"
 ALT="$M_S= 120.001^\circ$">|; 

$key = q/1.674;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1845.png"
 ALT="$1.674$">|; 

$key = q/displaystyle{{bf{v}times{{bf{n}cdot{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$\displaystyle {\bf v}\times {\bf n}\cdot{\bf r}$">|; 

$key = q/150^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$150^\circ$">|; 

$key = q/{displaymath}frac{r}{a}=(1-4,e,cosM+4,e^2)^{1slash2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="\begin{displaymath}
\frac{r}{a} = (1-4 e \cos M + 4 e^2)^{1/2}.
\end{displaymath}">|; 

$key = q/-deltabeta=EF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1349.png"
 ALT="$-\delta\beta = EF$">|; 

$key = q/26.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1077.png"
 ALT="$26.4'$">|; 

$key = q/28.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1125.png"
 ALT="$28.0'$">|; 

$key = q/6.588;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1244.png"
 ALT="$6.588$">|; 

$key = q/displaystyle-deltaa,cosmu,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1354.png"
 ALT="$\displaystyle - \delta a \cos\mu,$">|; 

$key = q/KSL;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="$KSL$">|; 

$key = q/04';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="$04'$">|; 

$key = q/Z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$Z$">|; 

$key = q/26.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1089.png"
 ALT="$26.8'$">|; 

$key = q/22.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img945.png"
 ALT="$22.0'$">|; 

$key = q/-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1681.png"
 ALT="$-1$">|; 

$key = q/r';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2019.png"
 ALT="$r'$">|; 

$key = q/T';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1654.png"
 ALT="$T'$">|; 

$key = q/2.4860;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2153.png"
 ALT="$2.4860$">|; 

$key = q/12.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img950.png"
 ALT="$12.2'$">|; 

$key = q/deltah_{pm}(360^circ-mu)=deltah_{pm}(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2157.png"
 ALT="$\delta h_{\pm}(360^\circ-\mu) = \delta h_{\pm}(\mu)$">|; 

$key = q/20.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="$20.6'$">|; 

$key = q/e=0.0167;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$e=0.0167$">|; 

$key = q/+5^circ23';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="$+5^\circ 23'$">|; 

$key = q/17^circ34';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="$17^\circ 34'$">|; 

$key = q/-5^circ28';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$-5^\circ 28'$">|; 

$key = q/63^circ52';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1387.png"
 ALT="$63^\circ 52'$">|; 

$key = q/22.6^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2001.png"
 ALT="$22.6^\circ$">|; 

$key = q/22.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img969.png"
 ALT="$22.8'$">|; 

$key = q/m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="$m$">|; 

$key = q/49.237;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="$49.237$">|; 

$key = q/-73.144;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1527.png"
 ALT="$-73.144$">|; 

$key = q/{displaymath}F=bar{F}+q=247.938-7.345=240.593simeq241^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2062.png"
 ALT="\begin{displaymath}
F = \bar{F} + q = 247.938-7.345 = 240.593\simeq 241^\circ.
\end{displaymath}">|; 

$key = q/30^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$30^\circ$">|; 

$key = q/displaystylebar{lambda}+q_1+q_2+q_3+q_4+q_5.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1209.png"
 ALT="$\displaystyle \bar{\lambda} + q_1+q_2+q_3+q_4+q_5.$">|; 

$key = q/displaystyle2,e,sinM+(5slash4),e^2,sin,2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="$\displaystyle 2 e \sin M + (5/4) e^2 \sin 2M,$">|; 

$key = q/02.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img961.png"
 ALT="$02.6'$">|; 

$key = q/-1^circ59';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$-1^\circ 59'$">|; 

$key = q/+5.51;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1413.png"
 ALT="$+5.51$">|; 

$key = q/17.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1094.png"
 ALT="$17.0'$">|; 

$key = q/xi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1732.png"
 ALT="$\xi$">|; 

$key = q/22.8^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2007.png"
 ALT="$22.8^\circ$">|; 

$key = q/displaystyle+coslambda,cosA,{{bf{s}times{{bf{e}cdot{{bf{r}-coslambda,sinA,{{bf{s}times{{bf{n}cdot{{bf{r}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$\displaystyle +\cos\lambda \cos A {\bf s}\times {\bf e}\cdot{\bf r} -\cos\lambda \sin A {\bf s}\times {\bf n}\cdot{\bf r}.$">|; 

$key = q/18^h29^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="$18^h29^m$">|; 

$key = q/displaystyledeltatheta_-(mu);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1689.png"
 ALT="$\displaystyle \delta\theta_-(\mu)$">|; 

$key = q/rho^2-2,e,a,cosM,rho-a^2,(1-e^2)=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="$\rho^2-2 e a \cos M \rho -a^2 (1-e^2)=0$">|; 

$key = q/+2.3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$+2.3$">|; 

$key = q/z_{{rm{min}=bar{z}-deltaz;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1676.png"
 ALT="$z_{\rm min} = \bar{z} - \delta z$">|; 

$key = q/displaystylefrac{1-zeta_S}{1-zeta},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1882.png"
 ALT="$\displaystyle \frac{1-\zeta_S}{1-\zeta},$">|; 

$key = q/{displaymath}q(23^circ)=2.561^circ,mbox{hspace{0.5cm}}zeta(23^circ)=4.913times10^{-2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="317" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1851.png"
 ALT="\begin{displaymath}
q(23^\circ)= 2.561^\circ,\mbox{\hspace{0.5cm}}\zeta(23^\circ)=4.913\times 10^{-2}.
\end{displaymath}">|; 

$key = q/37.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1114.png"
 ALT="$37.6'$">|; 

$key = q/49.280;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="$49.280$">|; 

$key = q/displaystyle+(1slash2),xi,(xi+1).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1696.png"
 ALT="$\displaystyle + (1/2) \xi (\xi+1).$">|; 

$key = q/alpha_0=90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\alpha_0=90^\circ$">|; 

$key = q/{displaymath}lambda=bar{lambda}+q+theta=115.416+2.561-5.883=112.094simeq112^circ06'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1860.png"
 ALT="\begin{displaymath}
\lambda=\bar{\lambda} + q + \theta= 115.416+2.561-5.883=112.094 \simeq 112^\circ 06'.
\end{displaymath}">|; 

$key = q/z=bar{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1683.png"
 ALT="$z=\bar{z}$">|; 

$key = q/bar{h}~~~~;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2156.png"
 ALT="$\bar{h}&nbsp;&nbsp;&nbsp;&nbsp;$">|; 

$key = q/h=Theta_-,deltah_-+bar{h}+Theta_+,deltah_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2051.png"
 ALT="$h = \Theta_- \delta h_-+ \bar{h}
+ \Theta_+ \delta h_+$">|; 

$key = q/-324.261;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1916.png"
 ALT="$-324.261$">|; 

$key = q/a_2=2bar{D}-M_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1471.png"
 ALT="$a_2=2\bar{D} - M_M$">|; 

$key = q/09^circ47';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="$09^\circ 47'$">|; 

$key = q/displaystyleE+e,sinE+(1slash4),e^2,sin2E.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="$\displaystyle E + e \sin E + (1/4) e^2 \sin 2 E.$">|; 

$key = q/12^h17^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="$12^h17^m$">|; 

$key = q/30.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="$30.6'$">|; 

$key = q/CP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="$CP$">|; 

$key = q/Deltat;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="$\Delta t$">|; 

$key = q/120^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$120^\circ$">|; 

$key = q/43.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img989.png"
 ALT="$43.4'$">|; 

$key = q/34.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1012.png"
 ALT="$34.2'$">|; 

$key = q/tanlambda,cosepsilon=sinalpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\tan\lambda \cos \epsilon = \sin \alpha$">|; 

$key = q/01.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img919.png"
 ALT="$01.2'$">|; 

$key = q/SL=a-(3slash2),e,a,cosM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="$SL = a-(3/2) e a \cos M$">|; 

$key = q/displaystyledeltah_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2034.png"
 ALT="$\displaystyle \delta h_+$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{epsfilesslashepicycle.eps}}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img1787.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{epsfiles/epicycle.eps}}
\end{figure}">|; 

$key = q/1.952;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1893.png"
 ALT="$1.952$">|; 

$key = q/-03';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1380.png"
 ALT="$-03'$">|; 

$key = q/Y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$Y$">|; 

$key = q/+70^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="$+70^\circ 00'$">|; 

$key = q/60^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$60^\circ$">|; 

$key = q/+35^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="$+35^\circ$">|; 

$key = q/{{bf{s};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="${\bf s}$">|; 

$key = q/Theta_+=0.759;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2086.png"
 ALT="$\Theta_+ = 0.759$">|; 

$key = q/{displaymath}M=lambda+77.213^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="\begin{displaymath}
M = \lambda + 77.213^\circ.
\end{displaymath}">|; 

$key = q/+7^circ12';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="$+7^\circ 12'$">|; 

$key = q/18.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1148.png"
 ALT="$18.8'$">|; 

$key = q/{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="${\bf r}$">|; 

$key = q/ell1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="$e\ll 1$">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=0.045times0.589+34.482+0.855times0.607=35.027^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1933.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
...+ = 0.045\times 0.589+34.482+0.855\times 0.607 = 35.027^\circ.
\end{displaymath}">|; 

$key = q/+58^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="$+58^\circ 26'$">|; 

$key = q/q_1=5.555^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1316.png"
 ALT="$q_1=5.555^\circ$">|; 

$key = q/-epsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$-\epsilon$">|; 

$key = q/deltaz=0.07059;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1856.png"
 ALT="$\delta z = 0.07059$">|; 

$key = q/displaystylesindelta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\displaystyle \sin\delta$">|; 

$key = q/displaystyledeltalambda;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1353.png"
 ALT="$\displaystyle \delta\lambda$">|; 

$key = q/24.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1005.png"
 ALT="$24.0'$">|; 

$key = q/42.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img959.png"
 ALT="$42.4'$">|; 

$key = q/265.600;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="$265.600$">|; 

$key = q/a=0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$a=0^\circ$">|; 

$key = q/248^circ46';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$248^\circ 46'$">|; 

$key = q/displaystyle-sinAleft[cosL,cosepsilon+sinL,sinepsilon,sin(alpha-t)right].;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$\displaystyle -\sin A\left[\cos L \cos\epsilon + \sin L \sin\epsilon \sin(\alpha-t)\right].$">|; 

$key = q/26^circ49';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$26^\circ 49'$">|; 

$key = q/297.661;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1751.png"
 ALT="$297.661$">|; 

$key = q/{displaymath}beta=h,beta_0=-1.038times1.615=-1.676simeq-1^circ41'.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2067.png"
 ALT="\begin{displaymath}
\beta = h \beta_0 = -1.038\times 1.615 = -1.676 \simeq -1^\circ 41'.
\end{displaymath}">|; 

$key = q/{displaymath}theta=Theta_-,deltatheta_-+bar{theta}+Theta_+,deltatheta_+=-0.113times5.980-32.007-0.077times8.955=-30.642^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="572" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1785.png"
 ALT="\begin{displaymath}
\theta = \Theta_- \delta\theta_- + \bar{\theta}+\Theta_+ \...
...= -0.113\times 5.980-32.007-0.077\times 8.955 = -30.642^\circ.
\end{displaymath}">|; 

$key = q/23^circ33';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$23^\circ 33'$">|; 

$key = q/+2.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="$+2.0$">|; 

$key = q/0.52407118;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$0.52407118$">|; 

$key = q/-0^circ15';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2126.png"
 ALT="$-0^\circ 15'$">|; 

$key = q/1.219;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1496.png"
 ALT="$1.219$">|; 

$key = q/53^circ15';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1382.png"
 ALT="$53^\circ 15'$">|; 

$key = q/11';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="$11'$">|; 

$key = q/01^circ16';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$01^\circ 16'$">|; 

$key = q/90^circ-|L+epsilon|;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$90^\circ - \vert L + \epsilon\vert$">|; 

$key = q/23^circ51';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$23^\circ 51'$">|; 

$key = q/{displaymath}beta_{S}=88.57'+deltabeta_1(M_M)+deltabeta_2(M_M)+deltabeta_3(M_S).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="363" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1601.png"
 ALT="\begin{displaymath}
\beta_{S} = 88.57' + \delta\beta_1(M_M)+\delta\beta_2 (M_M)+\delta\beta_3(M_S).
\end{displaymath}">|; 

$key = q/360slash0.98564735=325.24;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="$360/0.98564735 = 325.24$">|; 

$key = q/Msimeq321^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1752.png"
 ALT="$M\simeq 321^\circ$">|; 

$key = q/ast;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="$\ast$">|; 

$key = q/bar{F}_M(^circ);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1480.png"
 ALT="$\bar{F}_M(^\circ)$">|; 

$key = q/53.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img978.png"
 ALT="$53.0'$">|; 

$key = q/22.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img951.png"
 ALT="$22.2'$">|; 

$key = q/rho_{M,0}=R_Mslasha_M=1743,{{rm{km}slash384,399,{{rm{km}simeq15.59';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="370" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1554.png"
 ALT="$\rho_{M 0} = R_M/a_M =1743 {\rm km}/384,399 {\rm km}\simeq 15.59'$">|; 

$key = q/lambda_c=sin^{-1}(cosLslashsinepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\lambda_c=\sin^{-1}(\cos L/\sin\epsilon)$">|; 

$key = q/displaystyle2,e,sin,M+(5slash4),e^{,2},sin,2M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1878.png"
 ALT="$\displaystyle 2 e \sin  M + (5/4) e^{ 2} \sin 2M,$">|; 

$key = q/44.8';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1031.png"
 ALT="$44.8'$">|; 

$key = q/|L|>90^circ-epsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\vert L\vert&gt; 90^\circ - \epsilon$">|; 

$key = q/alpha_0=-90^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\alpha_0=-90^\circ$">|; 

$key = q/165^circ58';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1383.png"
 ALT="$165^\circ 58'$">|; 

$key = q/1slash4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$1/4$">|; 

$key = q/RPslashRQ=bslasha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="$RP/RQ = b/a$">|; 

$key = q/53';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="$53'$">|; 

$key = q/-3^circ03';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2142.png"
 ALT="$-3^\circ 03'$">|; 

$key = q/0.017;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1846.png"
 ALT="$0.017$">|; 

$key = q/alpha_c=cos^{-1}(1slashtanL,tanepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$\alpha_c=\cos^{-1}(1/\tan L \tan\epsilon)$">|; 

$key = q/+20^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="$+20^\circ 00'$">|; 

$key = q/58.0';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1128.png"
 ALT="$58.0'$">|; 

$key = q/R_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1555.png"
 ALT="$R_M$">|; 

$key = q/-2^circ03';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="$-2^\circ 03'$">|; 

$key = q/bar{lambda}_0=252.087^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1990.png"
 ALT="$\bar{\lambda}_0 = 252.087^\circ$">|; 

$key = q/47.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1109.png"
 ALT="$47.4'$">|; 

$key = q/25.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1047.png"
 ALT="$25.4'$">|; 

$key = q/{displaymath}tsimeqt_0+162+9.583slash0.46157617simeqt_0+183,{{rm{JD}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1794.png"
 ALT="\begin{displaymath}
t\simeq t_0+162+9.583/0.46157617\simeq t_0 + 183 {\rm JD}.
\end{displaymath}">|; 

$key = q/displaystylefrac{cosepsilon,cosdelta,sinalpha+sinepsilon,sindelta}{cosdelta,cosalpha}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\displaystyle \frac{\cos\epsilon \cos\delta \sin\alpha+\sin\epsilon \sin\delta}{\cos\delta \cos\alpha}.$">|; 

$key = q/-171.295;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="$-171.295$">|; 

$key = q/displaystylee'cos,M'-e'^{,2}sin^2,M';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1671.png"
 ALT="$\displaystyle e'\cos M' -e'^{ 2}\sin^2 M'$">|; 

$key = q/deltarightarrow-delta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$\delta\rightarrow -\delta$">|; 

$key = q/displaystylefrac{cosepsilon,cosbeta,sinlambda-sinepsilon,sinbeta}{cosbeta,coslambda}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle \frac{\cos\epsilon \cos\beta \sin\lambda-\sin\epsilon \sin\beta }{\cos\beta \cos\lambda}.$">|; 

$key = q/180^circ-lambda_c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$180^\circ-\lambda_c$">|; 

$key = q/mu=114.286^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2053.png"
 ALT="$\mu= 114.286^\circ$">|; 

$key = q/-6^circ08';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$-6^\circ 08'$">|; 

$key = q/-78.390;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1530.png"
 ALT="$-78.390$">|; 

$key = q/tilde{n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="$\tilde{n}$">|; 

$key = q/{{bf{u};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="${\bf u}$">|; 

$key = q/31';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="$31'$">|; 

$key = q/+23^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="$+23^\circ 26'$">|; 

$key = q/09^circ09';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$09^\circ 09'$">|; 

$key = q/{displaymath}t=t_0+530-0.244slash0.46157617=t_0+529.5,{{rm{JD},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1803.png"
 ALT="\begin{displaymath}
t=t_0+530-0.244/0.46157617=t_0+529.5 {\rm JD},
\end{displaymath}">|; 

$key = q/displaystylebar{lambda}+q.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="$\displaystyle \bar{\lambda} + q.$">|; 

$key = q/06.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1069.png"
 ALT="$06.2'$">|; 

$key = q/displaystylecosalpha_0,{{bf{u}-sinalpha_0,{{bf{v}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle \cos \alpha_0  {\bf u} -\sin \alpha_0 {\bf v}.$">|; 

$key = q/2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1886.png"
 ALT="$2'$">|; 

$key = q/M=100^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1339.png"
 ALT="$M=100^\circ$">|; 

$key = q/-189.128;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1914.png"
 ALT="$-189.128$">|; 

$key = q/+55^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="$+55^\circ 00'$">|; 

$key = q/1.675;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1844.png"
 ALT="$1.675$">|; 

$key = q/38.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1132.png"
 ALT="$38.2'$">|; 

$key = q/18';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="$18'$">|; 

$key = q/11.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img926.png"
 ALT="$11.4'$">|; 

$key = q/tanL,tandelta>1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$\tan L \tan\delta &gt; 1$">|; 

$key = q/13^h14^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$13^h 14^m$">|; 

$key = q/1.323;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1497.png"
 ALT="$1.323$">|; 

$key = q/muequivPG'B;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1658.png"
 ALT="$\mu\equiv PG'B$">|; 

$key = q/40.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="$40.6'$">|; 

$key = q/13^h56^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="$13^h56^m$">|; 

$key = q/08.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1141.png"
 ALT="$08.6'$">|; 

$key = q/zeta_S(M_S)=1.662times10^{-2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1764.png"
 ALT="$\zeta_S(M_S)= 1.662\times 10^{-2}$">|; 

$key = q/1.306;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1499.png"
 ALT="$1.306$">|; 

$key = q/-27.752;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1267.png"
 ALT="$-27.752$">|; 

$key = q/Msimeq88^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1778.png"
 ALT="$M\simeq 88^\circ$">|; 

$key = q/+5.00;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1410.png"
 ALT="$+5.00$">|; 

$key = q/displaystyle{{bf{v}times{{bf{e}cdot{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="$\displaystyle {\bf v}\times {\bf e}\cdot{\bf r}$">|; 

$key = q/~~0^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$&nbsp;&nbsp;0^\circ$">|; 

$key = q/41.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img929.png"
 ALT="$41.4'$">|; 

$key = q/PiSCA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$\Pi S C A$">|; 

$key = q/-178.701;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1272.png"
 ALT="$-178.701$">|; 

$key = q/46.4^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1989.png"
 ALT="$46.4^\circ$">|; 

$key = q/-991.943;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1775.png"
 ALT="$-991.943$">|; 

$key = q/deltatheta_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1723.png"
 ALT="$\delta\theta_-$">|; 

$key = q/5';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1218.png"
 ALT="$5'$">|; 

$key = q/+80^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$+80^\circ $">|; 

$key = q/-31';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1404.png"
 ALT="$-31'$">|; 

$key = q/15^h25^m;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$15^h25^m$">|; 

$key = q/tilde{D}=bar{lambda}-lambda_S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1222.png"
 ALT="$\tilde{D}=\bar{\lambda}-\lambda_S$">|; 

$key = q/+0^circ42';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="$+0^\circ 42'$">|; 

$key = q/displaystyle{{bf{s};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle {\bf s}$">|; 

$key = q/{displaymath}deltatheta_-(208^circ)=-0.447^circ,mbox{hspace{0.5cm}}bar{theta}(20space{0.5cm}}deltatheta_+(208^circ)=-0.522^circ.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1830.png"
 ALT="\begin{displaymath}
\delta\theta_-(208^\circ) = -0.447^\circ,\mbox{\hspace{0.5cm...
...\mbox{\hspace{0.5cm}}\delta\theta_+(208^\circ) = -0.522^\circ.
\end{displaymath}">|; 

$key = q/t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$t$">|; 

$key = q/58.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1146.png"
 ALT="$58.6'$">|; 

$key = q/88.9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="$88.9$">|; 

$key = q/18.9^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2005.png"
 ALT="$18.9^\circ$">|; 

$key = q/+78^circ26';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="$+78^\circ 26'$">|; 

$key = q/~-6^circ44';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$&nbsp;-6^\circ 44'$">|; 

$key = q/YEF;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1352.png"
 ALT="$YEF$">|; 

$key = q/alpha_0=180^circ+sin^{-1}(tanL,tanepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\alpha_0=180^\circ + \sin ^{-1}(\tan L \tan\epsilon)$">|; 

$key = q/alpha_c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\alpha_c$">|; 

$key = q/t-t_0=2,453,495.5-2,451,545.0=1,950.5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="$t-t_0 = 2 453 495.5-2 451 545.0=1 950.5$">|; 

$key = q/39.2';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1162.png"
 ALT="$39.2'$">|; 

$key = q/lambda_S=273.055^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1265.png"
 ALT="$\lambda_S = 273.055^\circ$">|; 

$key = q/24.6';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1023.png"
 ALT="$24.6'$">|; 

$key = q/displaystylesinL,sindelta+cosL,cosdelta,cost,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle \sin L \sin\delta + \cos L \cos\delta \cos t,$">|; 

$key = q/01.4';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img925.png"
 ALT="$01.4'$">|; 

$key = q/displaystyleq_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1199.png"
 ALT="$\displaystyle q_1$">|; 

$key = q/+05^circ00';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="$+05^\circ 00'$">|; 

$key = q/deltaz=0.06512;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1833.png"
 ALT="$\delta z = 0.06512$">|; 

1;

