Cislunar Mean-Motion Resonances: Definitions, Widths, and Comparisons with Resonant Satellites

Abstract: Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO, forming stable-unstable orbit 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 planar, circular, restricted three-body problem (PCR3BP) 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 high-fidelity 3-dimensional ephemeris propagation of several spacecraft - TESS, IBEX, and Spektr-R - in these regions is made, which shows good agreement with the simplified CR3BP model.