Orbit design for circumlunar formation flying

Finding relative orbits for satellite formations flying around the Earth, which are long-term bounded under various perturbations, has been a vibrant field of study. However, much less attention has been given to detecting such orbits for circumlunar formation flying missions. As opposed to low-Earth orbits, in circumlunar missions the third-body effect is large, and the magnitude of the C₂₂ sectorial harmonic has the same order as the J₂ zonal harmonic. This renders the analysis of bounded relative orbits more challenging. In this paper, we detect a new family of long-term bounded circumlunar relative orbits, which can be used for circumlunar formation flying missions. The main idea is to utilize the benefits of circumlunar frozen orbits, and operate the satellite formation in the vicinity of such orbits. This enables to find an analytical solution for the mean relative distance among the formation satellites, and use it to derive formation geometries that are resilient to the gravitational and third-body perturbations. Two invariant mean-distance conditions and one bounded mean-distance conditions are derived. Numerical simulations indicate that the newly-derived invariance conditions yield long-term bounded relative motion.