Revisiting Filtered and Closed-Form Solutions for Perturbed Geostationary Orbits

Abstract. The general equations for the geostationary orbit of a satellite subjected to perturbing forces are written: the filtered state is introduced as the difference between the true state and the geostationary state. The final equations contain nonlinear terms (both in the Keplerian terms and in the per- turbing forces) which are omitted in the linearized version. A general analytical, closed form solution in terms of unit initial conditions and of forcing terms is provided, with spe- cial attention for the effect of tesseral harmonics. Numerical examples are carried out to discuss the limits of acceptability of the linearized solution.