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Mercury

The ecliptic longitude of Mercury can be determined with the aid of Tables 62-64. Table 62 allows the mean longitude, $\bar{\lambda}$, and the mean anomaly, $M$, of Mercury to be calculated as functions of time. Next, Table 63 permits the equation of center, $q$, and the radial anomaly, $\zeta$, to be determined as functions of the mean anomaly. Finally, Table 64 allows the quantities $\delta\theta_-$, $\bar{\theta}$, and $\delta\theta_+$ to be calculated as functions of the epicyclic anomaly, $\mu$. The procedure for using the tables is analogous to the previously described procedure for using the Venus tables. One example of this procedure is given below.

 
Example: May 5, 2005 CE, 00:00 UT:
 
From Cha. 8, $t-t_0=1\,950.5$ JD, $\lambda_S = 44.602^\circ$, and $\zeta_S= -8.56\times 10^{-3}$. Making use of Table 62, we find:
     
$t$(JD) $ \bar{\lambda}(^\circ)$ $M(^\circ)$
     
+1000 $132.377$ $132.334$
+900 $83.139$ $83.101$
+50 $204.619$ $204.617$
+.5 $2.046$ $2.046$
Epoch $252.087$ $174.693$
  $647.268$ $596.791$
Modulus $314.268$ $236.791$
     

Given that $M\simeq 237^\circ$, Table 63 yields

\begin{displaymath}
q(237^\circ)= -16.974^\circ, \mbox{\hspace{0.5cm}}\zeta(237^\circ)=-1.367\times 10^{-1},
\end{displaymath}

so

\begin{displaymath}
\mu=\bar{\lambda}+q-\bar{\lambda}_S = 314.268-16.974-44.602= 252.692\simeq
253^\circ.
\end{displaymath}

It follows from Table 64 that

\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}

Now,

\begin{displaymath}
z= (1-\zeta_S)/(1-\zeta) = (1+8.56\times 10^{-3})/(1+1.367\times 10^{-1}) =
0.8873.
\end{displaymath}

However, from Table 5, $\bar{z}= 1.04774$ and $\delta z = 0.23216$, so

\begin{displaymath}
\xi = (\bar{z}-z)/\delta z = (1.04774-0.8873)/0.23216 \simeq 0.69.
\end{displaymath}

According to Table 17,

\begin{displaymath}
\Theta_-(0.69) = 0.107, \mbox{\hspace{0.5cm}}\Theta_+(0.69) = 0.583,
\end{displaymath}

so

\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}

Finally,

\begin{displaymath}
\lambda=\bar{\lambda}_S + \theta= 44.602-25.642=18.960 \simeq 18^\circ 58'.
\end{displaymath}

Thus, the ecliptic longitude of Mercury at 00:00 UT on May 5, 2005 CE was 18AR58.

The conjunctions and elongations of Mercury can be investigated using analogous methods to those employed earlier to examine the conjunctions and elongations of Venus. We find that the mean time period between successive superior, or inferior, conjunctions of Mercury is 116 days. On average, the greatest eastern and western elongations of Mercury occur when the epicyclic anomaly takes the values $\mu=111.7^\circ$ and $248.3^\circ$, respectively. Furthermore, the mean value of the greatest eastern or western elongation is $21.7^\circ$. Finally, the mean time period between a greatest eastern elongation and the following inferior conjunction, or between the inferior conjunction and the following greatest western elongation, is 22 JD. The conjunctions and elongations of Mercury during the years 2000-2002 CE are shown in Table 65.


Table 58: Mean motion of Venus. Here, $\Delta t = t-t_0$, $\Delta\bar{\lambda} = \bar{\lambda}-\bar{\lambda}_0$, $\Delta M = M - M_0$, and $\Delta\bar{F}= \bar{F}-\bar{F}_0$. At epoch ( $t_0= 2\,451\,545.0$ JD), $\bar{\lambda}_0 = 181.973^\circ$, $M_0 = 49.237^\circ$, and $\bar{F}_0 =105.253^\circ$.
$\Delta t$(JD) $\Delta\bar{\lambda}(^\circ)$ $\Delta M(^\circ)$ $\Delta \bar{F}(^\circ)$ $\Delta t$(JD) $\Delta\bar{\lambda}(^\circ)$ $\Delta M(^\circ)$ $\Delta \bar{F}(^\circ)$
               
10,000 181.687 181.304 181.381 1,000 162.169 162.130 162.138
20,000 3.374 2.608 2.761 2,000 324.337 324.261 324.276
30,000 185.062 183.912 184.142 3,000 126.506 126.391 126.414
40,000 6.749 5.216 5.523 4,000 288.675 288.522 288.552
50,000 188.436 186.520 186.904 5,000 90.844 90.652 90.690
60,000 10.123 7.824 8.284 6,000 253.012 252.782 252.828
70,000 191.810 189.128 189.665 7,000 55.181 54.913 54.966
80,000 13.498 10.432 11.046 8,000 217.350 217.043 217.105
90,000 195.185 191.736 192.426 9,000 19.518 19.174 19.243
               
100 160.217 160.213 160.214 10 16.022 16.021 16.021
200 320.434 320.426 320.428 20 32.043 32.043 32.043
300 120.651 120.639 120.641 30 48.065 48.064 48.064
400 280.867 280.852 280.855 40 64.087 64.085 64.086
500 81.084 81.065 81.069 50 80.108 80.107 80.107
600 241.301 241.278 241.283 60 96.130 96.128 96.128
700 41.518 41.491 41.497 70 112.152 112.149 112.150
800 201.735 201.704 201.710 80 128.173 128.170 128.171
900 1.952 1.917 1.924 90 144.195 144.192 144.192
               
1 1.602 1.602 1.602 0.1 0.160 0.160 0.160
2 3.204 3.204 3.204 0.2 0.320 0.320 0.320
3 4.807 4.806 4.806 0.3 0.481 0.481 0.481
4 6.409 6.409 6.409 0.4 0.641 0.641 0.641
5 8.011 8.011 8.011 0.5 0.801 0.801 0.801
6 9.613 9.613 9.613 0.6 0.961 0.961 0.961
7 11.215 11.215 11.215 0.7 1.122 1.121 1.121
8 12.817 12.817 12.817 0.8 1.282 1.282 1.282
9 14.420 14.419 14.419 0.9 1.442 1.442 1.442



Table 59: Deferential anomalies of Venus.
$M(^\circ)$ $q(^\circ)$ $100\,\zeta$ $M(^\circ)$ $q(^\circ)$ $100\,\zeta$ $M(^\circ)$ $q(^\circ)$ $100\,\zeta$ $M(^\circ)$ $q(^\circ)$ $100\,\zeta$
0 0.000 0.678 90 0.777 -0.005 180 0.000 -0.678 270 -0.777 -0.005
2 0.027 0.677 92 0.776 -0.028 182 -0.027 -0.677 272 -0.776 0.019
4 0.055 0.676 94 0.774 -0.052 184 -0.054 -0.676 274 -0.775 0.043
6 0.082 0.674 96 0.772 -0.075 186 -0.080 -0.674 276 -0.773 0.066
8 0.109 0.671 98 0.768 -0.099 188 -0.107 -0.671 278 -0.770 0.090
10 0.136 0.667 100 0.764 -0.122 190 -0.134 -0.668 280 -0.766 0.113
12 0.163 0.663 102 0.758 -0.145 192 -0.160 -0.663 282 -0.761 0.137
14 0.189 0.657 104 0.752 -0.168 194 -0.186 -0.658 284 -0.755 0.160
16 0.216 0.651 106 0.745 -0.191 196 -0.212 -0.652 286 -0.748 0.183
18 0.242 0.644 108 0.737 -0.214 198 -0.238 -0.645 288 -0.741 0.205
20 0.268 0.636 110 0.728 -0.236 200 -0.263 -0.637 290 -0.732 0.228
22 0.293 0.628 112 0.718 -0.258 202 -0.289 -0.629 292 -0.722 0.250
24 0.318 0.618 114 0.707 -0.279 204 -0.313 -0.620 294 -0.712 0.272
26 0.343 0.608 116 0.695 -0.301 206 -0.338 -0.610 296 -0.701 0.293
28 0.367 0.597 118 0.683 -0.322 208 -0.362 -0.599 298 -0.688 0.315
30 0.391 0.586 120 0.670 -0.342 210 -0.385 -0.588 300 -0.675 0.335
32 0.414 0.573 122 0.656 -0.362 212 -0.409 -0.576 302 -0.662 0.356
34 0.437 0.560 124 0.641 -0.382 214 -0.431 -0.563 304 -0.647 0.376
36 0.460 0.547 126 0.625 -0.401 216 -0.453 -0.550 306 -0.631 0.395
38 0.481 0.532 128 0.609 -0.420 218 -0.475 -0.536 308 -0.615 0.414
40 0.502 0.517 130 0.592 -0.438 220 -0.496 -0.521 310 -0.598 0.433
42 0.523 0.502 132 0.574 -0.456 222 -0.516 -0.506 312 -0.580 0.451
44 0.543 0.485 134 0.555 -0.473 224 -0.536 -0.490 314 -0.562 0.468
46 0.562 0.468 136 0.536 -0.490 226 -0.555 -0.473 316 -0.543 0.485
48 0.580 0.451 138 0.516 -0.506 228 -0.574 -0.456 318 -0.523 0.502
50 0.598 0.433 140 0.496 -0.521 230 -0.592 -0.438 320 -0.502 0.517
52 0.615 0.414 142 0.475 -0.536 232 -0.609 -0.420 322 -0.481 0.532
54 0.631 0.395 144 0.453 -0.550 234 -0.625 -0.401 324 -0.460 0.547
56 0.647 0.376 146 0.431 -0.563 236 -0.641 -0.382 326 -0.437 0.560
58 0.662 0.356 148 0.409 -0.576 238 -0.656 -0.362 328 -0.414 0.573
60 0.675 0.335 150 0.385 -0.588 240 -0.670 -0.342 330 -0.391 0.586
62 0.688 0.315 152 0.362 -0.599 242 -0.683 -0.322 332 -0.367 0.597
64 0.701 0.293 154 0.338 -0.610 244 -0.695 -0.301 334 -0.343 0.608
66 0.712 0.272 156 0.313 -0.620 246 -0.707 -0.279 336 -0.318 0.618
68 0.722 0.250 158 0.289 -0.629 248 -0.718 -0.258 338 -0.293 0.628
70 0.732 0.228 160 0.263 -0.637 250 -0.728 -0.236 340 -0.268 0.636
72 0.741 0.205 162 0.238 -0.645 252 -0.737 -0.214 342 -0.242 0.644
74 0.748 0.183 164 0.212 -0.652 254 -0.745 -0.191 344 -0.216 0.651
76 0.755 0.160 166 0.186 -0.658 256 -0.752 -0.168 346 -0.189 0.657
78 0.761 0.137 168 0.160 -0.663 258 -0.758 -0.145 348 -0.163 0.663
80 0.766 0.113 170 0.134 -0.668 260 -0.764 -0.122 350 -0.136 0.667
82 0.770 0.090 172 0.107 -0.671 262 -0.768 -0.099 352 -0.109 0.671
84 0.773 0.066 174 0.080 -0.674 264 -0.772 -0.075 354 -0.082 0.674
86 0.775 0.043 176 0.054 -0.676 266 -0.774 -0.052 356 -0.055 0.676
88 0.776 0.019 178 0.027 -0.677 268 -0.776 -0.028 358 -0.027 0.677
90 0.777 -0.005 180 0.000 -0.678 270 -0.777 -0.005 360 -0.000 0.678



Table 60: Epicyclic anomalies of Venus. All quantities are in degrees. Note that $\bar{\theta}(360^\circ - \mu) =-\bar{\theta}(\mu)$, and $\delta\theta_{\pm}(360^\circ-\mu) = -\delta\theta_{\pm}(\mu)$.
$\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$ $\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$ $\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$ $\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$
0 0.000 0.000 0.000 45 0.267 18.694 0.274 90 0.629 35.875 0.649 135 1.344 46.305 1.408
1 0.006 0.420 0.006 46 0.273 19.100 0.281 91 0.640 36.217 0.660 136 1.369 46.320 1.434
2 0.011 0.839 0.012 47 0.280 19.505 0.288 92 0.650 36.557 0.671 137 1.393 46.317 1.461
3 0.017 1.259 0.017 48 0.286 19.910 0.294 93 0.661 36.893 0.682 138 1.418 46.294 1.489
4 0.023 1.679 0.023 49 0.293 20.314 0.301 94 0.672 37.227 0.693 139 1.444 46.252 1.517
5 0.028 2.098 0.029 50 0.300 20.717 0.308 95 0.683 37.558 0.705 140 1.470 46.188 1.546
6 0.034 2.518 0.035 51 0.307 21.119 0.315 96 0.694 37.886 0.717 141 1.496 46.102 1.575
7 0.040 2.937 0.041 52 0.313 21.521 0.322 97 0.706 38.210 0.729 142 1.523 45.992 1.605
8 0.045 3.357 0.046 53 0.320 21.921 0.329 98 0.718 38.531 0.741 143 1.550 45.857 1.636
9 0.051 3.776 0.052 54 0.327 22.321 0.336 99 0.729 38.849 0.753 144 1.577 45.695 1.667
10 0.057 4.195 0.058 55 0.334 22.720 0.344 100 0.742 39.164 0.766 145 1.605 45.505 1.698
11 0.062 4.614 0.064 56 0.341 23.119 0.351 101 0.754 39.474 0.779 146 1.632 45.284 1.730
12 0.068 5.033 0.070 57 0.348 23.516 0.358 102 0.766 39.781 0.792 147 1.660 45.032 1.762
13 0.074 5.452 0.076 58 0.355 23.912 0.366 103 0.779 40.084 0.805 148 1.688 44.745 1.794
14 0.079 5.870 0.082 59 0.363 24.308 0.373 104 0.792 40.383 0.818 149 1.715 44.422 1.827
15 0.085 6.289 0.087 60 0.370 24.702 0.381 105 0.805 40.677 0.832 150 1.742 44.060 1.859
16 0.091 6.707 0.093 61 0.377 25.095 0.388 106 0.818 40.968 0.846 151 1.769 43.657 1.892
17 0.097 7.125 0.099 62 0.385 25.487 0.396 107 0.832 41.253 0.860 152 1.795 43.210 1.924
18 0.102 7.543 0.105 63 0.392 25.879 0.404 108 0.846 41.534 0.875 153 1.820 42.716 1.955
19 0.108 7.960 0.111 64 0.400 26.269 0.411 109 0.860 41.810 0.890 154 1.844 42.173 1.986
20 0.114 8.378 0.117 65 0.407 26.658 0.419 110 0.874 42.081 0.905 155 1.867 41.577 2.015
21 0.120 8.795 0.123 66 0.415 27.045 0.427 111 0.889 42.346 0.920 156 1.888 40.923 2.043
22 0.126 9.212 0.129 67 0.423 27.432 0.435 112 0.904 42.606 0.936 157 1.906 40.210 2.069
23 0.131 9.628 0.135 68 0.431 27.817 0.443 113 0.919 42.860 0.952 158 1.921 39.433 2.092
24 0.137 10.045 0.141 69 0.439 28.201 0.452 114 0.934 43.108 0.968 159 1.933 38.587 2.112
25 0.143 10.461 0.147 70 0.447 28.583 0.460 115 0.950 43.349 0.985 160 1.942 37.669 2.128
26 0.149 10.876 0.153 71 0.455 28.964 0.468 116 0.966 43.585 1.002 161 1.945 36.675 2.140
27 0.155 11.292 0.159 72 0.463 29.344 0.477 117 0.983 43.813 1.019 162 1.943 35.599 2.146
28 0.161 11.707 0.165 73 0.471 29.722 0.485 118 1.000 44.034 1.037 163 1.934 34.437 2.145
29 0.167 12.121 0.172 74 0.480 30.099 0.494 119 1.017 44.248 1.055 164 1.918 33.186 2.137
30 0.173 12.536 0.178 75 0.488 30.474 0.503 120 1.034 44.453 1.074 165 1.893 31.840 2.119
31 0.179 12.950 0.184 76 0.497 30.847 0.512 121 1.052 44.651 1.093 166 1.859 30.396 2.091
32 0.185 13.363 0.190 77 0.506 31.219 0.521 122 1.070 44.840 1.112 167 1.814 28.850 2.050
33 0.191 13.776 0.196 78 0.514 31.589 0.530 123 1.089 45.021 1.132 168 1.758 27.200 1.996
34 0.197 14.189 0.203 79 0.523 31.958 0.539 124 1.108 45.191 1.152 169 1.688 25.442 1.926
35 0.203 14.601 0.209 80 0.532 32.324 0.548 125 1.127 45.353 1.173 170 1.604 23.577 1.840
36 0.209 15.013 0.215 81 0.541 32.689 0.558 126 1.147 45.503 1.194 171 1.505 21.604 1.735
37 0.216 15.424 0.222 82 0.551 33.052 0.567 127 1.167 45.644 1.216 172 1.391 19.526 1.612
38 0.222 15.834 0.228 83 0.560 33.412 0.577 128 1.188 45.772 1.238 173 1.261 17.347 1.468
39 0.228 16.245 0.235 84 0.569 33.771 0.587 129 1.209 45.889 1.260 174 1.116 15.071 1.305
40 0.234 16.654 0.241 85 0.579 34.127 0.597 130 1.230 45.994 1.284 175 0.956 12.707 1.123
41 0.241 17.063 0.248 86 0.589 34.482 0.607 131 1.252 46.085 1.307 176 0.783 10.266 0.922
42 0.247 17.472 0.254 87 0.599 34.834 0.617 132 1.275 46.163 1.331 177 0.598 7.760 0.707
43 0.254 17.880 0.261 88 0.609 35.183 0.628 133 1.297 46.226 1.356 178 0.404 5.202 0.478
44 0.260 18.287 0.267 89 0.619 35.530 0.638 134 1.321 46.274 1.382 179 0.204 2.610 0.242
45 0.267 18.694 0.274 90 0.629 35.875 0.649 135 1.344 46.305 1.408 180 0.000 0.000 0.000



Table 61: The conjunctions and greatest elongations of Venus during the years 2000-2015 CE.
Event Date $\lambda$ Elongation
Superior Conjunction 11/06/2000 20GE46
Greatest Elongation 17/01/2001 14PI23 $47.1^\circ$ E
Inferior Conjunction 30/03/2001 09AR36
Greatest Elongation 08/06/2001 01TA39 $45.8^\circ$ W
Superior Conjunction 14/01/2002 23CP59
Greatest Elongation 22/08/2002 15LI08 $46.0^\circ$ E
Inferior Conjunction 31/10/2002 07SC58
Greatest Elongation 11/01/2003 03SG31 $47.0^\circ$ W
Superior Conjunction 18/08/2003 25LE20
Greatest Elongation 29/03/2004 25TA04 $46.0^\circ$ E
Inferior Conjunction 08/06/2004 17GE52
Greatest Elongation 17/08/2004 09CN29 $45.8^\circ$ W
Superior Conjunction 31/03/2005 10AR33
Greatest Elongation 03/11/2005 28SG27 $47.1^\circ$ E
Inferior Conjunction 13/01/2006 23CP36
Greatest Elongation 25/03/2006 18AQ07 $46.5^\circ$ W
Superior Conjunction 27/10/2006 04SC13
Greatest Elongation 09/06/2007 03LE20 $45.4^\circ$ E
Inferior Conjunction 18/08/2007 24LE45
Greatest Elongation 28/10/2007 18VI19 $46.5^\circ$ W
Superior Conjunction 09/06/2008 18GE41
Greatest Elongation 14/01/2009 12PI03 $47.1^\circ$ E
Inferior Conjunction 27/03/2009 07AR19
Greatest Elongation 05/06/2009 29AR25 $45.8^\circ$ W
Superior Conjunction 11/01/2010 21CP24
Greatest Elongation 19/08/2010 12LI49 $46.0^\circ$ E
Inferior Conjunction 29/10/2010 05SC34
Greatest Elongation 08/01/2011 01SG06 $47.0^\circ$ W
Superior Conjunction 16/08/2011 23LE13
Greatest Elongation 27/03/2012 22TA50 $46.0^\circ$ E
Inferior Conjunction 06/06/2012 15GE43
Greatest Elongation 15/08/2012 07CN18 $45.8^\circ$ W
Superior Conjunction 28/03/2013 08AR12
Greatest Elongation 01/11/2013 26SG02 $47.1^\circ$ E
Inferior Conjunction 11/01/2014 21CP08
Greatest Elongation 23/03/2014 15AQ44 $46.5^\circ$ W
Superior Conjunction 25/10/2014 01SC51
Greatest Elongation 06/06/2015 01LE09 $45.4^\circ$ E
Inferior Conjunction 15/08/2015 22LE33
Greatest Elongation 26/10/2015 16VI02 $46.4^\circ$ W



Table 62: Mean motion of Mercury. Here, $\Delta t = t-t_0$, $\Delta\bar{\lambda} = \bar{\lambda}-\bar{\lambda}_0$, $\Delta M = M - M_0$, and $\Delta\bar{F}= \bar{F}-\bar{F}_0$. At epoch ( $t_0= 2\,451\,545.0$ JD), $\bar{\lambda}_0 = 252.087^\circ$, $M_0 = 174.693^\circ$, and $\bar{F}_0 = 204.436^\circ$.
$\Delta t$(JD) $\Delta\bar{\lambda}(^\circ)$ $\Delta M(^\circ)$ $\Delta \bar{F}(^\circ)$ $\Delta t$(JD) $\Delta\bar{\lambda}(^\circ)$ $\Delta M(^\circ)$ $\Delta \bar{F}(^\circ)$
               
10,000 243.770 243.344 243.422 1,000 132.377 132.334 132.342
20,000 127.541 126.688 126.844 2,000 264.754 264.669 264.684
30,000 11.311 10.032 10.266 3,000 37.131 37.003 37.027
40,000 255.081 253.376 253.688 4,000 169.508 169.338 169.369
50,000 138.852 136.720 137.110 5,000 301.885 301.672 301.711
60,000 22.622 20.063 20.533 6,000 74.262 74.006 74.053
70,000 266.392 263.407 263.955 7,000 206.639 206.341 206.395
80,000 150.162 146.751 147.377 8,000 339.016 338.675 338.738
90,000 33.933 30.095 30.799 9,000 111.393 111.010 111.080
               
100 49.238 49.233 49.234 10 40.924 40.923 40.923
200 98.475 98.467 98.468 20 81.848 81.847 81.847
300 147.713 147.700 147.703 30 122.771 122.770 122.770
400 196.951 196.934 196.937 40 163.695 163.693 163.694
500 246.189 246.167 246.171 50 204.619 204.617 204.617
600 295.426 295.401 295.405 60 245.543 245.540 245.541
700 344.664 344.634 344.640 70 286.466 286.463 286.464
800 33.902 33.868 33.874 80 327.390 327.387 327.387
900 83.139 83.101 83.108 90 8.314 8.310 8.311
               
1 4.092 4.092 4.092 0.1 0.409 0.409 0.409
2 8.185 8.185 8.185 0.2 0.818 0.818 0.818
3 12.277 12.277 12.277 0.3 1.228 1.228 1.228
4 16.370 16.369 16.369 0.4 1.637 1.637 1.637
5 20.462 20.462 20.462 0.5 2.046 2.046 2.046
6 24.554 24.554 24.554 0.6 2.455 2.455 2.455
7 28.647 28.646 28.646 0.7 2.865 2.865 2.865
8 32.739 32.739 32.739 0.8 3.274 3.274 3.274
9 36.831 36.831 36.831 0.9 3.683 3.683 3.683



Table 63: Deferential anomalies of Mercury.
$M(^\circ)$ $q(^\circ)$ $100\,\zeta$ $M(^\circ)$ $q(^\circ)$ $100\,\zeta$ $M(^\circ)$ $q(^\circ)$ $100\,\zeta$ $M(^\circ)$ $q(^\circ)$ $100\,\zeta$
0 0.000 20.564 90 22.900 -4.229 180 0.000 -20.564 270 -22.900 -4.229
2 1.086 20.544 92 22.677 -4.896 182 -0.663 -20.555 272 -23.100 -3.551
4 2.169 20.487 94 22.433 -5.552 184 -1.326 -20.528 274 -23.276 -2.864
6 3.247 20.391 96 22.168 -6.197 186 -1.987 -20.483 276 -23.428 -2.168
8 4.316 20.257 98 21.884 -6.831 188 -2.647 -20.420 278 -23.553 -1.463
10 5.376 20.085 100 21.580 -7.452 190 -3.304 -20.340 280 -23.652 -0.750
12 6.422 19.876 102 21.259 -8.062 192 -3.959 -20.242 282 -23.723 -0.030
14 7.454 19.631 104 20.920 -8.659 194 -4.610 -20.126 284 -23.764 0.697
16 8.467 19.350 106 20.566 -9.243 196 -5.257 -19.993 286 -23.775 1.429
18 9.460 19.035 108 20.195 -9.815 198 -5.900 -19.842 288 -23.755 2.165
20 10.431 18.685 110 19.809 -10.373 200 -6.538 -19.675 290 -23.703 2.905
22 11.377 18.303 112 19.409 -10.918 202 -7.170 -19.490 292 -23.617 3.648
24 12.298 17.889 114 18.996 -11.450 204 -7.796 -19.288 294 -23.497 4.392
26 13.190 17.445 116 18.569 -11.969 206 -8.417 -19.070 296 -23.342 5.137
28 14.052 16.971 118 18.129 -12.473 208 -9.030 -18.835 298 -23.150 5.880
30 14.882 16.469 120 17.677 -12.964 210 -9.637 -18.583 300 -22.922 6.621
32 15.680 15.941 122 17.212 -13.441 212 -10.236 -18.316 302 -22.656 7.359
34 16.443 15.388 124 16.737 -13.904 214 -10.827 -18.032 304 -22.353 8.091
36 17.171 14.811 126 16.250 -14.353 216 -11.410 -17.733 306 -22.010 8.818
38 17.862 14.212 128 15.752 -14.787 218 -11.985 -17.418 308 -21.629 9.536
40 18.517 13.593 130 15.243 -15.207 220 -12.552 -17.087 310 -21.208 10.245
42 19.133 12.954 132 14.724 -15.613 222 -13.109 -16.741 312 -20.748 10.942
44 19.710 12.299 134 14.196 -16.004 224 -13.657 -16.380 314 -20.249 11.628
46 20.249 11.628 136 13.657 -16.380 226 -14.196 -16.004 316 -19.710 12.299
48 20.748 10.942 138 13.109 -16.741 228 -14.724 -15.613 318 -19.133 12.954
50 21.208 10.245 140 12.552 -17.087 230 -15.243 -15.207 320 -18.517 13.593
52 21.629 9.536 142 11.985 -17.418 232 -15.752 -14.787 322 -17.862 14.212
54 22.010 8.818 144 11.410 -17.733 234 -16.250 -14.353 324 -17.171 14.811
56 22.353 8.091 146 10.827 -18.032 236 -16.737 -13.904 326 -16.443 15.388
58 22.656 7.359 148 10.236 -18.316 238 -17.212 -13.441 328 -15.680 15.941
60 22.922 6.621 150 9.637 -18.583 240 -17.677 -12.964 330 -14.882 16.469
62 23.150 5.880 152 9.030 -18.835 242 -18.129 -12.473 332 -14.052 16.971
64 23.342 5.137 154 8.417 -19.070 244 -18.569 -11.969 334 -13.190 17.445
66 23.497 4.392 156 7.796 -19.288 246 -18.996 -11.450 336 -12.298 17.889
68 23.617 3.648 158 7.170 -19.490 248 -19.409 -10.918 338 -11.377 18.303
70 23.703 2.905 160 6.538 -19.675 250 -19.809 -10.373 340 -10.431 18.685
72 23.755 2.165 162 5.900 -19.842 252 -20.195 -9.815 342 -9.460 19.035
74 23.775 1.429 164 5.257 -19.993 254 -20.566 -9.243 344 -8.467 19.350
76 23.764 0.697 166 4.610 -20.126 256 -20.920 -8.659 346 -7.454 19.631
78 23.723 -0.030 168 3.959 -20.242 258 -21.259 -8.062 348 -6.422 19.876
80 23.652 -0.750 170 3.304 -20.340 260 -21.580 -7.452 350 -5.376 20.085
82 23.553 -1.463 172 2.647 -20.420 262 -21.884 -6.831 352 -4.316 20.257
84 23.428 -2.168 174 1.987 -20.483 264 -22.168 -6.197 354 -3.247 20.391
86 23.276 -2.864 176 1.326 -20.528 266 -22.433 -5.552 356 -2.169 20.487
88 23.100 -3.551 178 0.663 -20.555 268 -22.677 -4.896 358 -1.086 20.544
90 22.900 -4.229 180 0.000 -20.564 270 -22.900 -4.229 360 -0.000 20.564



Table 64: Epicyclic anomalies of Mercury. All quantities are in degrees. Note that $\bar{\theta}(360^\circ - \mu) =-\bar{\theta}(\mu)$, and $\delta\theta_{\pm}(360^\circ-\mu) = -\delta\theta_{\pm}(\mu)$.
$\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$ $\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$ $\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$ $\mu$ $\delta\theta_-$ $\bar{\theta}~~~~$ $\delta\theta_+$
0 0.000 0.000 0.000 45 1.711 11.702 2.403 90 3.450 20.277 5.113 135 4.257 19.475 7.325
1 0.038 0.270 0.052 46 1.749 11.941 2.459 91 3.486 20.395 5.177 136 4.237 19.267 7.327
2 0.075 0.540 0.104 47 1.788 12.179 2.515 92 3.522 20.509 5.241 137 4.214 19.048 7.324
3 0.113 0.809 0.156 48 1.827 12.415 2.572 93 3.557 20.618 5.305 138 4.188 18.818 7.317
4 0.150 1.079 0.208 49 1.866 12.650 2.628 94 3.592 20.722 5.368 139 4.159 18.578 7.304
5 0.188 1.348 0.260 50 1.905 12.882 2.685 95 3.627 20.822 5.432 140 4.127 18.326 7.286
6 0.225 1.618 0.313 51 1.944 13.114 2.742 96 3.662 20.917 5.496 141 4.092 18.064 7.262
7 0.263 1.887 0.365 52 1.983 13.343 2.799 97 3.696 21.007 5.559 142 4.053 17.791 7.233
8 0.301 2.156 0.417 53 2.022 13.571 2.857 98 3.729 21.091 5.623 143 4.011 17.506 7.197
9 0.338 2.425 0.469 54 2.061 13.797 2.914 99 3.762 21.171 5.686 144 3.966 17.210 7.155
10 0.376 2.693 0.521 55 2.100 14.021 2.972 100 3.795 21.246 5.749 145 3.917 16.903 7.106
11 0.414 2.961 0.574 56 2.139 14.244 3.030 101 3.827 21.315 5.812 146 3.865 16.585 7.050
12 0.451 3.229 0.626 57 2.178 14.464 3.088 102 3.858 21.378 5.874 147 3.809 16.255 6.986
13 0.489 3.497 0.678 58 2.217 14.683 3.146 103 3.889 21.436 5.937 148 3.749 15.914 6.915
14 0.527 3.764 0.731 59 2.257 14.899 3.205 104 3.919 21.488 5.999 149 3.686 15.561 6.836
15 0.564 4.031 0.783 60 2.296 15.113 3.263 105 3.949 21.534 6.060 150 3.619 15.197 6.749
16 0.602 4.298 0.836 61 2.335 15.326 3.322 106 3.977 21.575 6.121 151 3.548 14.822 6.654
17 0.640 4.564 0.889 62 2.374 15.536 3.381 107 4.005 21.609 6.182 152 3.473 14.436 6.549
18 0.678 4.829 0.941 63 2.413 15.743 3.441 108 4.032 21.636 6.242 153 3.394 14.039 6.436
19 0.716 5.094 0.994 64 2.453 15.949 3.500 109 4.059 21.658 6.301 154 3.311 13.630 6.314
20 0.753 5.359 1.047 65 2.492 16.152 3.560 110 4.084 21.673 6.360 155 3.224 13.211 6.182
21 0.791 5.622 1.100 66 2.531 16.353 3.620 111 4.109 21.681 6.418 156 3.133 12.780 6.041
22 0.829 5.886 1.153 67 2.570 16.551 3.680 112 4.132 21.682 6.475 157 3.039 12.339 5.890
23 0.867 6.148 1.206 68 2.609 16.747 3.740 113 4.155 21.676 6.532 158 2.940 11.888 5.729
24 0.905 6.410 1.259 69 2.649 16.940 3.801 114 4.176 21.663 6.587 159 2.838 11.426 5.558
25 0.943 6.672 1.312 70 2.688 17.131 3.862 115 4.197 21.643 6.641 160 2.732 10.955 5.377
26 0.981 6.932 1.366 71 2.727 17.319 3.923 116 4.216 21.616 6.695 161 2.622 10.474 5.186
27 1.019 7.192 1.419 72 2.766 17.504 3.984 117 4.233 21.580 6.747 162 2.508 9.983 4.985
28 1.057 7.451 1.473 73 2.805 17.686 4.045 118 4.250 21.538 6.797 163 2.391 9.483 4.774
29 1.095 7.709 1.526 74 2.844 17.865 4.107 119 4.265 21.487 6.846 164 2.271 8.974 4.554
30 1.133 7.967 1.580 75 2.882 18.042 4.169 120 4.278 21.428 6.894 165 2.147 8.457 4.324
31 1.172 8.223 1.634 76 2.921 18.215 4.231 121 4.291 21.361 6.940 166 2.019 7.932 4.084
32 1.210 8.479 1.688 77 2.960 18.385 4.293 122 4.301 21.286 6.984 167 1.889 7.399 3.835
33 1.248 8.734 1.742 78 2.999 18.552 4.355 123 4.310 21.202 7.026 168 1.756 6.859 3.578
34 1.286 8.987 1.796 79 3.037 18.716 4.417 124 4.317 21.109 7.067 169 1.620 6.312 3.312
35 1.325 9.240 1.851 80 3.075 18.876 4.480 125 4.322 21.008 7.105 170 1.481 5.759 3.038
36 1.363 9.491 1.905 81 3.114 19.033 4.543 126 4.326 20.898 7.140 171 1.340 5.200 2.757
37 1.402 9.742 1.960 82 3.152 19.186 4.606 127 4.327 20.778 7.173 172 1.197 4.636 2.469
38 1.440 9.991 2.015 83 3.190 19.336 4.669 128 4.326 20.649 7.204 173 1.052 4.067 2.174
39 1.479 10.240 2.070 84 3.227 19.482 4.732 129 4.323 20.511 7.231 174 0.905 3.494 1.875
40 1.517 10.487 2.125 85 3.265 19.625 4.795 130 4.318 20.363 7.256 175 0.756 2.917 1.570
41 1.556 10.732 2.180 86 3.302 19.763 4.859 131 4.311 20.206 7.277 176 0.607 2.337 1.261
42 1.594 10.977 2.236 87 3.340 19.898 4.922 132 4.301 20.038 7.295 177 0.456 1.755 0.949
43 1.633 11.220 2.291 88 3.377 20.029 4.986 133 4.289 19.861 7.309 178 0.304 1.171 0.634
44 1.672 11.462 2.347 89 3.413 20.155 5.049 134 4.274 19.673 7.319 179 0.152 0.586 0.317
45 1.711 11.702 2.403 90 3.450 20.277 5.113 135 4.257 19.475 7.325 180 0.000 0.000 0.000



Table 65: The conjunctions and greatest elongations of Mercury during the years 2000-2002 CE.
Event Date $\lambda$ Elongation
Superior Conjunction 15/01/2000 25CP08
Greatest Elongation 15/02/2000 13PI44 $18.1^\circ$ E
Inferior Conjunction 01/03/2000 11PI23
Greatest Elongation 28/03/2000 10PI35 $27.9^\circ$ W
Superior Conjunction 09/05/2000 18TA59
Greatest Elongation 09/06/2000 13CN27 $24.2^\circ$ E
Inferior Conjunction 06/07/2000 14CN39
Greatest Elongation 27/07/2000 15CN03 $19.7^\circ$ W
Superior Conjunction 22/08/2000 29LE16
Greatest Elongation 06/10/2000 09SC17 $25.6^\circ$ E
Inferior Conjunction 30/10/2000 06SC58
Greatest Elongation 15/11/2000 04SC02 $19.3^\circ$ W
Superior Conjunction 25/12/2000 04CP18
Greatest Elongation 28/01/2001 27AQ07 $18.4^\circ$ E
Inferior Conjunction 13/02/2001 24AQ23
Greatest Elongation 11/03/2001 23AQ05 $27.5^\circ$ W
Superior Conjunction 23/04/2001 03TA22
Greatest Elongation 22/05/2001 24GE13 $22.6^\circ$ E
Inferior Conjunction 16/06/2001 25GE26
Greatest Elongation 09/07/2001 26GE18 $21.1^\circ$ W
Superior Conjunction 05/08/2001 13LE32
Greatest Elongation 19/09/2001 22LI50 $26.6^\circ$ E
Inferior Conjunction 14/10/2001 20LI51
Greatest Elongation 29/10/2001 17LI50 $18.5^\circ$ W
Superior Conjunction 04/12/2001 12SG45
Greatest Elongation 12/01/2002 10AQ33 $18.9^\circ$ E
Inferior Conjunction 27/01/2002 07AQ42
Greatest Elongation 21/02/2002 05AQ55 $26.6^\circ$ W
Superior Conjunction 07/04/2002 17AR27
Greatest Elongation 04/05/2002 04GE54 $21.0^\circ$ E
Inferior Conjunction 27/05/2002 05GE48
Greatest Elongation 21/06/2002 07GE04 $22.8^\circ$ W
Superior Conjunction 21/07/2002 28CN06
Greatest Elongation 01/09/2002 06LI10 $27.3^\circ$ E
Inferior Conjunction 27/09/2002 04LI35
Greatest Elongation 13/10/2002 01LI44 $18.0^\circ$ W
Superior Conjunction 14/11/2002 21SC39
Greatest Elongation 26/12/2002 24CP01 $19.8^\circ$ E



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Richard Fitzpatrick 2010-07-21