Low-Energy Boundaries on Vertical Motion Near the Secondary Body in the CR3BP

Trajectories at low energies with respect to the secondary body in the Circular Restricted Three-Body Problem are important for the future of orbital and landing missions. However, at these low energies, we demonstrate that high-latitude regions are unreachable for ballistic trajectories traveling through the L_1 and L_2 necks. This study explores the upper bound of vertical motion for these ballistic trajectories at a particular low energy. An initial grid-search across the L_1 and L_2 necks at Europa reveal that certain patterns appear in the trajectories that maximize inclination and out-of-plane velocity—metrics which are used to quantify vertical motion. These patterns are traced back to two nearby families of planar periodic orbits. These full families are generated and points of bifurcation are located. Certain families that originate as out-of-plane bifurcations from the two planar families are generated, and their unique members that match the energy of the grid-search are isolated. The manifolds of these particular periodic orbits exist along the simulated upper bound of vertical motion from the grid-search results. These results suggest that multiple families of stable and near-stable periodic orbits govern the flow of motion near this boundary.