Temporary capture about the Moon involving Sun–Earth libration point dynamics

This study investigates the mechanism of temporary capture about the Moon, either originating from periodic orbits or following bounce-back trajectories associated with the libration point dynamics of the Sun–Earth system. The primary objective is to analyze the maneuvers required for temporary capture and to explore possibilities for natural temporary capture in the Earth–Moon system. We begin by defining a temporary capture set, determining the maximum eccentricity allowed at perigee with respect to the Moon while satisfying a revolution constraint. Then, using an appropriate expansion, we examine temporary capture initiated from the Sun–Earth libration point regime, focusing on the value of the central in-plane amplitude of the libration point orbits. Next, we include the hyperbolic amplitudes of the expansion and explore temporary capture with orbits that bounce back in the libration point regime. Finally, based on these analyses, we propose a method for achieving low-energy natural capture trajectories departing from the Earth.