Cislunar Resonant Transport and Heteroclinic Pathways: From 3:1 to 2:1 to L1

Abstract: Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is critical for both lunar exploration and for high-Earth-orbiting trajectories. In this study, we investigate the role of mean-motion resonances and their associated heteroclinic connections in enabling natural semi-major axis transport in the Earth-Moon system. Working within the planar circular restricted three-body problem, we compute and analyze families of periodic orbits associated with the interior 4:1, 3:1, and 2:1 lunar resonances. These families exhibit a rich bifurcation structure, including transitions between prograde and retrograde branches and connections through collision orbits. We construct stable and unstable manifolds of the unstable resonant orbits using a perigee-based Poincar\'e map, and identify heteroclinic connections - both between resonant orbits and with lunar $L_1$ libration-point orbits - across a range of Jacobi constant values. Using a new generalized distance metric to quantify the closeness between trajectories, we establish operational times-of-flight for such heteroclinic-type orbit-to-orbit transfers. These connections reveal ballistic, zero-$\Delta v$ pathways that achieve major orbit changes within reasonable times-of-flight, thus defining a network of accessible semi-major axes. Our results provide a new dynamical framework for long-term spacecraft evolution and cislunar mission design, particularly in regimes where lunar gravity strongly perturbs high Earth orbits.