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

TL;DR

This paper defines and analyzes lunar mean-motion resonances in cislunar space, estimating their widths and influence zones using simplified models and validating findings with real spacecraft data.

Contribution

It provides a rigorous definition of resonance zones, estimates their widths in the PCR3BP model, and compares these with actual spacecraft trajectories, enhancing understanding of cislunar dynamics.

Findings

Resonance influence zones are broader than semi-analytical predictions.

Good agreement between simplified models and spacecraft ephemeris data.

Resonance zones significantly impact cislunar orbital stability.

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.