Minimum-Propellant Optimal Trajectories for the De-Orbiting of Decommissioned Satellites in Lunar Polar Graveyard Regions

NASA's ambitious plans for sustained human presence in cislunar space, e.g. the Lunar Orbital Platform-Gateway program, has raised interest in cislunar orbits, looking for some desirable properties such as relatively low transfer costs from Earth, low orbit maintenance costs, and favourable communications opportunities with both Earth and the lunar south pole. As the cislunar region is anticipated to become increasingly populated with spacecraft, including potential debris, it is important to highlight the necessity of strategic deorbiting planning and compliance with international laws governing space debris. This study focuses on optimizing lunar deorbiting trajectories that use electric propulsion and depart from a NRHO, with a particular emphasis on minimizing propellant usage. The chosen reference orbit is the Gateway's southern L2 NRHO, with perilune and apolune radii of 3,300 km and 70,000 km and 9:2 synodic resonance with respect to the Moon's orbit around Earth. The optimization is carried out by an indirect method based on the Optimal Control Theory that transforms the propellant minimization problem into a Two-Point Boundary Value Problem. The single-shooting method shows bang-bang control derived from the Pontryagin's Maximum Principle to optimize the trajectories, ensuring that a specific region in the lunar north pole is targeted. The dynamic model considers 3-body gravitation (spacecraft subject to Earth and Moon gravity) within the Circular Restricted Three-Body Problem. Results identify a specific orbital arc in the NRHO, post-apolune, which is deemed ideal for de-orbiting the satellite via a two-burn trajectory that enables direct disposal towards the lunar north pole, significantly reducing propellant consumption allowing the mission to allocate more fuel for earlier operational phases, effectively extending the mission's operational lifespan