Linearized equations for J2 perturbed motion relative to an elliptical orbit.

摘要

A set of linearized equations was derived for the motion, relative to an elliptical reference orbit, of an object influenced by J2 perturbations. Solutions from numerical simulations were used to compare these equations and the linearized Keplerian equations to the exact equations. The inclusion of the J2 perturbations in the derived linear equations increased the accuracy of the solution significantly in the out-of-orbit-plane direction, while the accuracy within the orbit plane remained roughly unchanged. These equations could be useful in the analysis of orbital rendezvous or formation flying problems.