Relative Motion Equations in the local-vertical local-Horizon Frame for Rendezvous in lunar Orbits

In this paper, a set of equations for relative motion description in lunar orbits is presented. The local-vertical local-horizon frame is selected to describe the relative dynamics of a chaser approaching a target in lunar orbit, allowing the development of relative guidance and navigation systems for rendezvous and docking. The model considers the Earth and Moon gravitational influence on the two spacecraft, which are assumed to have negligible masses. The proposed equations are intended for the study of rendezvous missions with a future cis-lunar space station, whose development is currently investigated by several space agencies as the next step for space exploration.