Momentum Maps and Transport Mechanisms in the Planar Circular Restricted Three-Body Problem

Transport mechanisms in the restricted three-body problem rely on the topology of dynamical structures created by gravitational interactions between a particle and the planets’ governing its motion. In a large part, periodic orbits and their associated invariant manifolds dictate the design of transfer trajectories between the neighborhoods of the two primaries. In this paper, the behavior of such dynamical structures is investigated using dynamical systems theory. Specifically, a Poincaré map is introduced utilizing the zero-momentum subspace of the third-body motion in the phase-space. Such a Poincaré map is called the momentum map. These maps complement existing knowledge of the dynamical structures in the planar circular restricted three-body problem. The dynamical structures arising from these zero-momentum surfaces identify transport opportunities to planar libration point orbits, and promote the development of a catalog of transfers in cislunar space. Through geometric analysis of the velocity surface, a visualization technique is developed that enables the identification of transport opportunities with little computational effort. This approach offers an effective technique for analyzing the geometry of transfers in cislunar space.