Design of distant retrograde orbits based on a higher order analytical solution

TL;DR

This paper develops a higher order analytical solution for distant retrograde orbits using perturbation methods, enabling more accurate and flexible orbit design beyond traditional resonance constraints.

Contribution

It introduces a novel higher order analytical approach for distant retrograde orbit design, expanding applicability to large librations and providing new design parameters.

Findings

Extended the analytical solution range for large librations

Enabled design of periodic retrograde orbits without 1:1 resonance constraint

Improved accuracy over previous rough approximations

Abstract

Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on perturbation methods and succeed in computing a higher order analytical solution that extends the range of applicability of previous solutions to the problem of relative, quasi-satellite orbits with large librations. Besides, the analytical solution provides two design parameters that are effectively used in the computation of periodic, distant retrograde orbits without constraining to the typical 1:1 resonance.