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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