Design Strategies for Short-Term Ballistic Loitering Near Multi-Body Orbits

Design techniques for short-term ballistic spacecraft loitering near multi-body orbits are developed and applied to the Gateway near rectilinear halo orbit. The first half of this paper extends previously introduced strategies for relative trajectory design that leverage principal stretching and restoring direction information. Where previous loitering analysis examined position-only initial state variations, the current work considers mixed-phase (position and velocity) ballistic loitering. This investigation demonstrates that the analytical interpretation of the loitering solutions persists when the relative velocity is nonzero, diversifying the resulting geometry and expanding the available design space. A numerical framework is then introduced to solve for initial relative states subject to general conditions imposed on the end states of a ballistic loitering trajectory. The framework is validated on the known geometric solutions in a simplified dynamical model before being demonstrated on a sample loitering scenario in a higher-fidelity ephemeris model. Numerical methods to populate the loitering solution space are summarized, with attention given to the relationship between the imposed loitering conditions and the dimensionality of the resulting solution manifold.