Global search and optimization for free-return Earth-Mars cyclers

A planetary cycler trajectory is a periodic orbit that shuttles a spaceship indefinitely between two or more planets, ideally using no powered maneuvers. Recently, the cycler concept has been revived as an alternative to the more traditional human-crewed Mars missions. This dissertation investigates a class of idealized Earth-Mars cyclers that are composed of Earth to Earth free-returns trajectories patched together with gravity- assisted flybys. A systematic method is presented to identify all feasible free-return trajectories following an arbitrary gravity-assisted flyby. The multiple-revolution Lambert’s Problem is solved in the context of half-rev, full-rev, and generic returns. The solutions are expressed geometrically, and the resulting velocity diagram is a mission-planning tool with applications including but not limited to Earth-Mars cyclers. Two different global search methods are then developed and applied, taking advantage of all three types of free-return solutions. The first method results in twenty- four ballistic cyclers with periods of two to four synodic periods, ninety-two ballistic cyclers with periods of five or six synodic periods, and hundreds of near-ballistic cyclers. Most of the solutions are previously undocumented. The second and more generalized method only searches for the more practical cyclers with repeat times of three-synodic periods or less. This global approach uses combinatorial analysis and minimax optimization to identify 203 promising ballistic or near-ballistic mostly new cyclers. Finally, the feasibility of accurate ephemeris versions of the promising idealized cyclers is demonstrated. An efficient optimization method that utilizes analytic gradients is developed for long duration, ballistic, patched-conic trajectories with multiple flybys. The approach is applied at every step of a continuation method that transitions the simple model solutions to accurate ephemeris solutions. Hundreds of ballistic launch opportunities for accurate ephemeris cyclers are documented. Remarkably, twenty parent cyclers are found to have an average total maneuver requirement over all twenty-one launch windows of less than 100 m/s for seven-cycle propagations. In summary, the Earth-Mars cycler problem is fully addressed from the problem definition stage all the way to solutions in a reasonably accurate ephemeris model for a broad class of cyclers. The most promising solutions are viable options for sustaining a Earth-Mars transportation system.