Optimizing the perilune of lunar landing trajectories using dynamical systems theory

The optimal perilune of a low-energy lunar landing trajectory is studied using invariant manifolds of the circular restricted three-body problem. The Sun-Earth-Moon-spacecraft restricted four-body system in the low-energy Earth-Moon transfer problem is divided into two coupled restricted three-body systems. The invariant manifolds of these two three-body systems are constructed to find the low-energy transfer trajectories for the spacecraft from a low earth parking orbit to an optimal perilune for minimizing descent landing propellant consumption. By analyzing the energy evolutions of the spacecraft's transfer trajectories in the perspective of dynamical systems theory, the desirable perilune with a low altitude and small arrival velocity has been optimized. A maneuver at the intersection of invariant manifolds between two three-body systems is needed to ensure the continuity of the manifolds, as well as to get a low cost approach to the Moon's surface. The energy analysis method can be extended to other three-body systems in the deep space low-energy landing trajectory design.