Low-Thrust Earth-Moon Transfer Trajectories to Stable Distant Retrograde Orbits using Indirect Optimization Method

This research focuses on identifying low-thrust optimal trajectories for inserting satellites into a Distant Retrograde Orbit (DRO) around the Moon with minimum propellant usage, contributing to cost-effective strategies and enabling heavier payloads for future cislunar missions. This study is motivated by the growing interest in establishing a scientific presence in cislunar space, with initiatives aiming to position orbital stations on such orbits, or to utilize lunar resources and create a launchpad for missions to Mars and beyond. NASA’s Artemis program is heading in this direction. Among potential locations, Periodic Orbits around Lagrangian Points, including DROs and Near-Rectilinear Halo Orbits (NRHOs), present promising options. DROs, in particular, offer significant advantages due to their stability, reducing maintenance costs and prolonging mission lifespans. To optimize DRO insertion trajectories, a Two-point Boundary Value Problem approach is employed. This method enhances solution convergence amid the chaotic gravitational dynamics between Earth and the Moon and includes an iterative shooting procedure with a bang-bang thrust control law derived from indirect optimal control theory. Pontryagin’s Maximum Principle is applied to ensure the optimality of control solutions. DRO computations are performed within the Circular Restricted Three-Body Problem (CR3BP) framework using a single-shooting method based on the State Transition Matrix analysis. This model accounts for the gravitational influences of the Moon, which significantly impacts both the injection trajectory and the stability of the DRO. Results indicate that two-burn finite-thrust trajectories present the most efficient means for direct DRO insertion from Earth, effectively exploiting the Earth-Moon gravitational interaction without the need of performing a lunar gravity assist or multiple swing-bys. The optimal trajectory is proven to be the one that best fits the shape of the orbit, inserting the satellite directly into the final stable DRO.