Satgen322  In Orbit Pt6   Planets    by GM4IHJ               27 May 95

When we need to calculate the position of a planet , there is a slight
complication. Planets orbit around the Sun , not the Earth. So we first
fix the Suns position as explained in Satgen321, then, we use the elements
of the orbit of the planet concerned to position it with respect to the
Sun . As with the Sun Earth orbit the planetary elements are stated in
standard polynomial form :-
      Ao  +  A1 *T   +  A2  *T  *T   +  A3  *T  *T  *T

Elements for Mercury at Epoch 1900 January 0.5 are :-

                                              * T           *T *T
Mean Longitude of Planet  L   178.179078   149474.07078   0.0003011

Semi major axis           a   0.3870986

Eccentricity              e   0.20561421   0.00002046    -0.000000030

Inclination               i   7.002881     0.0018608     -0.0000183

Argument of perihelion    w   28.753753    0.3702806      0.0001208

Right Ascension               47.145944    1.1852083      0.0001739

EG    L = 178.179078  + 149474.07078 * T   +  0.0003011 * T * T
Note.. Mercury and Venus have no *T*T*T term , in this simple form of the
elements , but the other planets do.

To get the element values at the date we require we calculate time T in
Julian centuries between Epoch date and date required, and substitute this
value of T into each polynomial.

Then with updated elements Mean Anomaly M = L - w - Right Ascension , and
knowing M and e we can solve Keplers equation and go on to work out the
rest of the Sun centred ( Heliocentric) coordinates for the planet. We
then convert these heliocentric coordinates to Earth centred (Geocentric)
coordinates so that we can track the planet from our earth station.

Simple distance data for the heliocentric coordinates are :-
Planet to Sun minimum distance (perhelion distance) = a(1 - e)
Planet to Sun Maximum distance (aphelion  distance) = a(1 + e)
and using the planet Sun coordinates and the Earth Sun coordinates we can
calculate Planet to Earth distance. Noting that these distances are
usually given in Astronomical Units where 1AU = Sun Earth separation of
about 93003000 miles. All this maths is done by the planetary tracking
software, but users need to be clear that Solar and Planetary tracking is
different from near earth satellite tracking. We cannot put Keplerian
elements for Mars or Mercury into our satellite software, and get accurate
solutions.