Analytical solution to perturbed geosynchronous orbit

An analytical solution to a perturbed geosynchronous orbit is presented and validated through numerical simulations. The Clohessy-Wiltshire equations are used to describe the small perturbation from the ideal geostationary orbit. The perturbing forces due to Earth gravity harmonics, solar-radiation pressure, and solar and lunar attraction are expanded in a suitable form for the analytical integration. Thus, solutions that were obtained are added to that of the reference motion to yield the complete solution. Fully nonlinear equations of the orbital motion are numerically integrated and the results are compared with those from the analytical solutions. It is shown that the analytical solutions may be used to propagate the orbital motion accurately up to several days, and the long-term secular trend is well predicted.