Automated Generation of Symmetric Lunar Free-Return Trajectories

Abstract

A procedure for free-return trajectory generation in a simplified Earth-moon system is presented. With two-body and circular restricted three-body models, the algorithm constructs an initial guess of the translunar injection state and time of flight. Once the initial trajectory is found, the Jacobian of the constraints is derived analytically using linear perturbation theory, and a square system of nonlinear equations is solved numerically to target Earth entry interface conditions leading to feasible free-return trajectories. No trial and error is required to generate the initial guess. Possible free returns include departures from both posigrade and retrograde Earth orbits coupled with circumlunar or cislunar flight, in and out of the Earth-moon plane.