Satgen321  In Orbit Pt5  The Sun      by GM4IHJ                 20 May 95

Recent satgens have considered satellites orbiting the earth, where it was
acceptable to ignore the mass of the satellite, and the effects due to
other bodies. When a satellite orbits far from earth , or, we consider the
orbit of a planet or moon, these short cuts are no longer permissable.
For this reason therefore the calculation of the orbit takes a somewhat
different form from the solution of NASA 2 line Keplerian elements used
for near earth satellites. The mathematics employs a roughly similar
format but Ephemeris data replaces NASA 2 line elements.

Equally important . When we get away from the earth , orbit periods become
months and years , not minutes. This becomes obvious when we start with
the Epoch time of the Ephemeris data. Because of the long time periods
involved it is common practice to set the Epoch at some cardinal point in
time Eg noon 1 Jan 1900 or , noon 1 Jan 2000. Orbits in deep space do not
suffer from the spasmodic drag factors present in low earth orbits so
predictions can be kept reasonably accurate over many years, with even the
perturbation due to the big planets Jupiter and Saturn being amenable to
simple correction. So if your software has Ephemeris data for Epoch noon 1
Jan 2000 it should be good , unchanged, for the next half century

Typical Ephemeris Data  - for the Earth orbit around the Sun

Epoch 1900 Jan 0.5  = noon 1st January 1900  (julian days start at noon)

Geometric mean longitude of Sun
L = 279.69668  + 36000.76892 *T  + 0.0003025 *T *T

Solar Mean Anomaly
M = 358.47583  + 35999.04975 *T  - 0.000150 *T *T  - 0.0000033 *T *T *T

Eccentricity of Earth orbit
e = 0.01675104 - 0.0000418 *T  - 0.000000126 *T *T

The variable T which we introduce to get the above ephemeris to show the
values of L, M and e for the date/time for which we want details , is the
number of Julian centuries which have elapsed between the above epoch for
1 jan 1900 , and, the date for which we want data. If readers are unsure
about using Julian day or century number, see satgens 250 and 251 .

Having worked out the revised L , M, and e , we can use the updated M and
e to solve Keplers Equation giving us the Eccentric Anomaly, from which we
can calculate the true anomaly v, and go on to get the Suns true longitude
which is L +v -M, and then to get the Solar radius vector  and the Earth
Sun distance. After which in the simple calculation format all the other
parameters we need to know such as Right Ascension , Declination, Azimuth
and Elevation , are obtainable. For those who need much greater accuracy ,
nutation and aberration can be considered but this will not normally be
required by ordinary users. In fact all this maths is just nice to know.
All the user needs to do is run the software , with its built in Ephemeris
data which will last for decades.