High Accuracy Relative Motion of Spacecraft Using Linearized Time-Varying J2-Perturbed Terms

This paper presents a set of linearized equations was derived for the motion, relative to an elliptical reference orbit, of an object influenced by J2 perturbation terms. Approximate solution for simulations was used to compare these equations and the linearized keplerian equations to the exact equations. The inclusion of the linearized perturbations in the derived equations increased the high accuracy of the solution significantly in the out-of-orbit-plane direction, while the accuracy within the orbit plane remained roughly unchanged. In fact, it will be determined whether the inclusion of this disturbance provides a significant increase in accuracy over Melton’s problem. By reason of using approximate terms in the solution, for continues accuracy increase of time-varying parameters, this solution could be useful in the element-errors evaluation and analysis of orbital multiple rendezvous or formation flying problem, that are involved to the short-period terms.