# Geostationary orbit propagator

sup3r_n00b
Hi guys,

I've been trying to make a longitude and drift rate propagator for a geostationary satellite but the equations do not take into account other perturbing forces apart from the Earth's triaxiality.

Longitude = Initial Longitude + Initial Drift Rate * Elapsed Time + 0.5 * Longitudinal Acceleration * (Elapsed Time)^2

Drift Rate = Initial Drift Rate + Longitudinal Acceleration * Elapsed Time

As you can see, the equations only consider the longitudinal acceleration of the satellite. I've compared the results using these equations from the results given by a flight dynamics software and it seems that there is a large dispcrepancy. I'm thinking that the above equations do not take into account the perturbations caused by the moon and the sun or other perturbations that I don't know about.

Can anyone please help me improve the accuracy of the propagator by adding the necessary corrections to the equation? I've been searching the internet for orbit propagators but all I've found are propagators for the orbital elements and the solution is quite complex. I know that the orbital elements can be converted into the longitude and drift rate but all I want is a simple equation that will directly predict the longitude at an elapsed time based from the initial longitude and drift rate.

Thanks and Regards,
sup3r_n00b

## Answers and Replies

Gold Member
I have not studied the details, but Montenbruck and Gill  describes a linearisation of the equations of motions for geostationary satellites that result in a set of ODE's known as Hill's equations or Clohessy-Wiltshire equations that can be integrated to a closed form solution involving secular and periodic oscillations. They also mention some software called GEODA for calculating such satellite tracks.

Perhaps this can provide you with more information you can search for.

 Satellite Orbits, Montenbruck and Gill, Springer, 2000.