Optimal Transfers from the L1 Halo Orbit of the Earth–Moon System to Earth

Designing direct-return orbits from the Earth–Moon space to Earth’s surface is critical for manned lunar missions and emergency returns. This paper investigates optimal transfer solutions from a halo orbit around the Earth–Moon L1 libration point to an Earth reentry point. Cislunar L1 orbits are commonly utilized as habitats for spacecraft involved in various missions, necessitating the development of a minimum-fuel transfer strategy between L1 orbits and Earth for future complex applications within the Earth–Moon system. We suggest a novel design method that leverages the accessibility of halo orbit pseudomanifolds to closer Earth orbits, enabling efficient transfers through a single impulsive maneuver along the unstable pseudomanifold trajectory. To overcome the challenge of local optima resulting from numerous optimization variables, we employ an enhanced particle swarm optimization with gray wolf optimizer algorithm. This method aims to minimize the Δ V transfer costs within the circular restricted 3-body problem framework. Our results demonstrate low and feasible flight times and are expected to provide valuable reference for the design and implementation of future Earth–Moon transfer orbits.