Geometric analysis of free-return trajectories following a gravity-assisted flyby

The purpose of this study is to systematically identify all feasible trajectories following a gravity-assisted flyby that immediately return to the flyby body with no intermediate maneuvers. Every class of possible transfer angles is considered including even-npi, odd-npi, and generic return orbits. Lambert's problem is solved for a desired time-of-flight range allowing the possibility for multiple spacecraft and celestial body revolutions. The solutions are expressed geometrically, and the resulting velocity diagram is a mission-planning tool with potential applications that include cycler trajectories and planetary moon tours. The generalized free-return solutions can be used to construct loitering orbits about one celestial body or transfers between multiple bodies. Several previously documented cycler trajectories are improved using the discussed solutions.