Second-Order Solution for Relative Motion on Eccentric Orbits in Curvilinear Coordinates
Abstract
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as the independent variable, and solved by the method of successive approximations. A comparison of error trends against eccentricity and inter-spacecraft separation is presented between the new solution and prominent Cartesian, curvilinear, and orbital element based solutions from the literature. The second-order curvilinear solution offers a thousand-fold improvement in accuracy over the first-order curvilinear solution, and still greater improvement over first- and second-order rectilinear solutions when large along-track separations are present.
Cite
@article{arxiv.1909.02146,
title = {Second-Order Solution for Relative Motion on Eccentric Orbits in Curvilinear Coordinates},
author = {Matthew Willis and Kyle T. Alfriend and Simone D'Amico},
journal= {arXiv preprint arXiv:1909.02146},
year = {2019}
}
Comments
Presented at 2019 AAS/AIAA Astrodynamics Specialist Conference