Investigation of Interior Mean Motion Resonances and Heteroclinic Connections in the Earth-Moon System

Abstract

Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is of significant importance for lunar exploration, as well as for design of high Earth-orbiting mission trajectories in other contexts. A key aspect of these dynamics is the presence of mean motion resonances, as heteroclinic connections between unstable resonant orbits are fundamental to changing and understanding the evolution over time of a spacecraft’s semimajor axis. In this paper, we first compute and analyze several important resonant orbit families within the Earth-Moon system based on the planar circular restricted 3-body problem. Focusing on interior resonances 4:1, 3:1, and 2:1, we identify a number of bifurcations of these resonances’ periodic orbit families. Once the aforementioned orbits are computed, we then compute their stable and unstable manifolds using an osculating orbit perigee Poincaré map. Carrying out these computations across a range of energy values, we are able to characterize the range of naturally attainable semimajor axis values for future distant Earth-bound or lunar spacecraft missions.