Inclusion effects of J2-perturbed motion over Melton's problem.

Purpose – The purpose of this paper is to analyze the inclusion effects of the linearized time-varying J2-perturbed terms for relative accuracy increase significantly over Melton's problem. Design/methodology/approach – The methodology is based on the previous studies provided by Ross's paper. He gives a set of equations based on the C-W equations which incorporates the J2 gravitational perturbations and states in his introduction that this method can be expanded for the elliptical reference orbits as described by Melton. Findings – One challenge in implementing the relative motions is maintaining the relations as it experiences gravitational perturbations, most notably due to non-spherical Earth. Simulation results show that the inclusion of time-varying J2 perturbation terms 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. Practical implications – By reason 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 limited orbit periods. Originality/value – The originality of this paper is to develop Melton's researches. He provided a method for generalizing the linear equations of motion to an elliptical orbit which enabled the determination of a time-explicit, approximate solution. In this regard, there is no paper which has evaluated the inclusion effects of the linearized time-varying J2 perturbation terms over Melton's equations with such an approach. [ABSTRACT FROM AUTHOR]