a Soleymani - Space Systems Academic Group, Shahid Beheshti University, Tehran, Iran
a Toloei - Department of Aerospace Engineering, Shahid Beheshti University, Evin, Tehran, Iran

This paper presents a set of linearized equations which was derived for the motion, relative to an elliptical reference orbit, of an object influenced by J 2 perturbation terms. Approximate solution forsimulations was used to compare these equations and the linearized keplerian equations to the exactequations. 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 thisdisturbance provides a significant increase in accuracy over Melton’s problem. Becuase of replacing approximate terms (e, M) in this solution, for continues accuracy increase of time-varying parameters containing θ(t) and RO(t) , this solution could be useful in the element-errors evaluation and analysis of orbital multiple rendezvous missions, that are involved to the short-period terms

Approximate Solution,Relative Motion,Spacecraft,Time-varying Terms,Linearized J2 Perturbations,Simulation Results