Circumlunar free-return trajectories: a patched-conics approach
A spacecraft on a free-return trajectory departs a primary body and is sent back to its vicinity by a gravity assist from a secondary body; in other words, after orbit injection, no additional propulsive maneuver is required for the return trip. Free-return trajectories between the Earth and the Moon, in particular, have been of great practical importance for both unmanned and manned missions since the beginning of the Space Age. In this post I discuss the construction of a circumlunar free-return trajectory by a patched-conics approach. For the Earth-Moon case, this type of analysis must account for the fact that a significant portion of the trajectory is spent inside the Sphere of Influence (SOI) of the Moon, whose extension cannot be neglected as in the case of heliocentric interplanetary missions. I will focus in particular on the method described in Section 9.3 of Battin (1999), which was originally published in a technical report from the early Apollo era [2]. Besides its hi...