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The ecliptic latitude of Mars can be determined with the aid of Tables 46, 67, and 68. Table 46 allows
the mean argument of latitude,
, of Mars to be calculated as a function of
time. Next, Table 67 permits the deferential latitude,
, to
be determined as a function of the true argument of latitude,
. Finally, Table 68 allows the quantities
,
, and
to be calculated as functions of the epicyclic
anomaly,
.
The procedure for using the tables is as follows:
- Determine the fractional Julian day number,
, corresponding to the date and time
at which the ecliptic latitude is to be calculated with the aid of Tables 27-29. Form
, where
is the epoch.
- Calculate the planetary equation
of center,
, ecliptic anomaly,
, and
interpolation parameters
and
using the
procedure set out in Cha. 8.
- Enter Table 46 with the digit for each power of 10
in
and take out the corresponding values of
. If
is negative then the corresponding
values are also negative.
The value of the mean argument of latitude,
, is the
sum of all the
values plus the value of
at the epoch.
- Form the true argument of latitude,
. Add as many multiples of
to
as is required to make it fall in the range
to
.
Round
to the nearest degree.
- Enter Table 67 with the value of
and take out the
corresponding value of the deferential latitude,
. It is necessary to interpolate if
is odd.
- Enter Table 68 with the value of
and take
out the corresponding values of
,
, and
. If
then it is necessary to make use
of the identities
and
.
- Form the epicyclic latitude correction factor,
.
- The ecliptic latitude,
, is the product of the deferential latitude,
, and the epicyclic latitude correction factor,
. The decimal fraction can
be converted into arc minutes
using Table 31. Round to the nearest arc minute.
One example of this procedure is given below.
Example: May 5, 2005 CE, 00:00 UT:
From Cha. 8,
JD,
,
,
, and
.
Making use of
Table 46, we find:
|
|
(JD) |
 |
|
|
+1000 |
 |
+900 |
 |
+50 |
 |
+.5 |
 |
Epoch |
 |
|
 |
Modulus |
 |
|
|
Thus,
It follows from Table 67 that
Since
, Table 68 yields
so
Finally,
Thus,
the ecliptic latitude of Mars at 00:00 UT on May 5, 2005 CE was
.
Next: Jupiter
Up: Planetary Latitudes
Previous: Determination of Ecliptic Latitude
Richard Fitzpatrick
2010-07-21