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.
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.
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.
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.
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.
