Resonance widths, chaotic zones, and transport in cislunar space

Abstract

Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO forming stable-unstable pairs, with corresponding intermingled chaotic and regular regions. The resonance zone is rigorously defined using the separatrix of unstable resonant periodic orbits surrounding stable quasi-periodic regions. Our study leverages the restricted three-body problem to estimate the (stable) resonance widths and (unstable) chaotic resonance zones of influence of the 2:1 and 3:1 MMRs across various Jacobi constants, employing a Poincar´e map at perigee and presenting findings in easily interpretable geocentric orbital elements. An analysis of the semi-major axis versus eccentricity plane reveals broader regions of resonance influence than those predicted by semi-analytical models based on the perturbed Kepler problem. A comparison with observed spacecraft in these regions is made, showing excellent agreement.