Relative Motion Dynamics in Restricted Three-Body Scenarios

This paper discusses the derivation and simplification of equation sets for the relative motion dynamics characterization in the restricted three-body problem. As opposed to previous models proposed in the literature, the relative motion is studied in a frame local to the target spacecraft, the local-vertical local-horizon frame, and spacecraft state is expressed with respect to the primary about which they are orbiting. The exact description of the relative dynamics is derived, as well as simplified equation sets based on both the elliptic and the circular restricted three-body problems. The accuracy of the simplified sets is analyzed by means of extensive numerical simulations on a realistic rendezvous scenario with a target on lunar orbit.