Systematic Method for Constructing Earth-Mars Cyclers Using Free-Return Trajectories

Abstract

A procedure for constructing idealized Earth-Mars cycler orbits in a simple solar system is presented. Solutions from the multiple-revolution Lambert problem are utilized to find free-return Mars trajectories. Multiple combinations of these generic return orbits are patched to sequences of full and half-revolution return orbits with Earth-generated gravity-assisted maneuvers. An algorithm is developed to find all useful combinations of the defined free returns that have a combined period of any integer multiple of the synodic period. Given a sequence of free returns, a procedure is then developed to minimize the maximum of all of the turning angles associated with the flybys necessary to maintain and reinitiate the cycler. The method identifies 24 ballistic cyclers with periods of two to four synodic periods, 92 ballistic cyclers with periods of five or six synodic periods, and hundreds of near-ballistic cyclers, where a ballistic cycler is defined to be one that requires no powered maneuvers to maintain and has realistic turning angles with respect to the surface of the Earth. These resulting orbits have diverse characteristics that could benefit a variety of potential missions. Although the method finds several known idealized cyclers, most of the orbits presented are previously undocumented.