Extended analysis on stability, capture, and escape for planar retrograde periodic orbit around Earth

Abstract

Cislunar space has been attracting interest as a strategic place to connect Earth and interplanetary space. This paper extends our previous analysis on the use of retrograde periodic orbits around Earth for staging orbits. The orbit of interest is found to be linearly stable against the luni-solar gravitational perturbation, yet its Moon-grazing geometry leads to modest \(\Delta v\) to capture into (escape from) the orbit via lunar flyby. In the analysis of capture trajectories, we globally search for transfer trajectories from the vicinity of Earth. It is found that Sun-perturbed, multi-revolutional transfer is a promising option to reduce the launch energy and insertion \(\Delta v\). In the escape analysis, transfer from the periodic orbit toward interplanetary space via powered Earth flyby is studied. Temporal insertion into an unstable periodic orbit that is in a retrograde \(1:1\) mean-motion resonance is found to be a favorable option to flexibly tune the escape direction.