Orbital Rendezvous and Spacecraft Loitering in the Earth-Moon System

To meet the challenges posed by future space exploration activities, relative satellite motion techniques and capabilities require development to incorporate dynamically complex regimes. Specific relative motion applications including orbital rendezvous and spacecraft loitering will play a significant role in NASA’s Gateway and Artemis missions which aim to land the first woman and next man on the Moon by 2024. In this investigation, relative motion in the restricted 3-body problem is formulated, validated, and tested in a rotating local-vertical-local-horizontal (LVLH) frame situated at a target spacecraft and followed by a chaser. Two formulations of the restricted 3-body problem are considered, namely the Circular Restricted 3-Body Problem (CR3BP) and the Elliptical Restricted 3-Body Problem (ER3BP). Comparisons between the relative dynamical models in the CR3BP and ER3BP, respectively, and other standard relative motion sets of equations such as the Euler-Hill (HCW) model and the Linear Equations of Relative Motion (LERM) are accomplished to identify limitations and inaccuracies pertaining to the in orbits that exist in the CR3BP and ER3BP, respectively. Additionally, the relative motion equations are linearized to develop computational tools for solutions to the rendezvous and space loitering problems in the Earth-Moon system