Medium-Energy, Retrograde, Ballistic Transfer to the Moon

This study analyzes a recently discovered new class of exterior transfers to the Moon under the perspective of lunar collision orbit dynamics. These transfers typically end with a retrograde ballistic capture, i.e., with negative Keplerian energy and angular momentum with respect to the Moon. Yet their Jacobi constant is relatively low, at which no forbidden regions exist, and the transfers do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth-Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, for which invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together the orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun-Earth system. The method is used to systematically reproduce the novel retrograde ballistic capture.