Comparison of relative orbital motion perturbation solutions in cartesian and spherical coordinates

Previously shown perturbation approaches for unperturbed spacecraft relative motion solutions in Cartesian and spherical coordinates, in which both the chief eccentricity and the normalized separation were treated as order ϵ, are extended in this work to allow for higher chief orbit eccentricity. The relative accuracies of the solutions obtained in Cartesian versus spherical coordinates are explored for a wide range of relative orbit scenarios and perturbation orders. While the use of spherical coordinates eliminates many of the secular terms in the Cartesian solution and extends the range of in-track separations, certain scenarios are found to result in less accuracy.