Fuel-optimal, low-thrust, three-dimensional Earth-Mars trajectories

Fuel-optimal three-dimensional trajectories from Earth to Mars for spacecra ft powered by a low-thrust rocket with variable specific impulse capability are presented. The problem formulation treats the spacecraft mass as a sta te variable, thus coupling the spacecraft design to the trajectory optimiza tion. Gravitational effects of the sun, Earth, and Mars are included throug hout an entire trajectory. To avoid numerical sensitivity, the trajectory i s divided into segments, each defined with respect to a different central b ody. These segments are patched at intermediate time points, with proper ma tching conditions on the states and costates. The optimization problem is s olved using an indirect multiple shooting method. Details of trajectories f or the outbound legs of crewed missions to Mars, with trip times of 145 and 168 days, are shown. Effects due to variations in the trip time, departure and arrival orbit inclinations, initial fuel mass, and power level are inv estigated.