No-return disposal trajectories in the Earth-Moon system: A parametric analysis

The growing interest in cislunar space shown in recent years, together with the increasing number of studies on missions targeting the Earth-Moon (EM) system, has raised numerous questions, both on how to operate such missions safely and on how to prevent the emergence of a debris problem in the region. The exponential growth in the number of objects orbiting near Earth has already threatened its long-term sustainability: it is necessary to prevent this from happening in the cislunar domain as well, which is additionally characterised by strong non-linear dynamics. The most effective way to mitigate the problem is to prevent it from happening in the first place, which can be achieved by developing efficient, robust and economically attractive End-of-Life (EoL) disposal solutions. This work investigates the dynamical behaviours of unstable manifold trajectories departing from Libration Point Orbits (LPOs) considered of interest for future cislunar missions. To understand how these can be leveraged on would then be the foundation of efficient disposal design. The objective is to identify how unstable manifold trajectories’ behaviours can be exploited to improve the cost-effectiveness, efficiency, and reliability of EoL disposal strategies when included in a more comprehensive study, performing a parametric analysis on various families of periodic orbits, developing maps that would allow operators, given certain constraints, to identify possible disposal options based on maximum Time of Flight (ToF) and available on-board fuel. To do so, unstable manifold trajectories of various periodic orbits, evaluated at different departure phase angles, are propagated for a maximum time of six months. Possible outcomes of propagation include crossing EM- L 2, impacting the Moon, intersecting an orbit around the Earth with a radius equal to that of the Geostationary (GEO) belt or remaining within the Zero Velocity Curves (ZVCs) of the EM system for the overall time frame considered. If the first outcome is achieved, the focus shifts to no-return escape trajectories from EM- L 2. After escape through the EM- L 2 bottleneck, a manoeuvre is applied to modify the trajectory’s energy so that the EM system’s ZVCs close, preventing the satellite from re-entering their inner region. The analysis is repeated for seven distinct families of LPOs: the Halo, Lyapunov and Vertical families in both EM- L 1 and L 2, together with the Butterfly family. The results of this work are maps showing how the trajectories evolve as a function of the phase angle of the starting point and its Jacobi Constant (JC), representing a preliminary dynamic cartography of escape behaviour in the EM system.