Fuel-optimal three-dimensional earth-mars trajectories with low-thrust exhaust-modulated plasma propulsion

This paper addresses the determination of fuel-optimal three-dimensional trajectories from Earth to Mars. for a spacecraft powered by a low-thrust rocket with variable specific impulse (I-sp) capability. The problem formulation treats the spacecraft mass as a state variable, thus coupling the spacecraft design to the trajectory optimization. Gravitational effects of the sun, Earth, and Mars are included throughout an entire trajectory. To avoid numerical sensitivity, the trajectory dynamics is divided into segments, each written with respect to a different central body. These segments are patched at intermediate time points, with proper matching conditions of the variables. The matching conditions for all the states, except the spacecraft mass, involve nonlinear transformations. The optimization problem is solved using an indirect multiple shooting method. Results for the outbound-legs of manned missions to Mars, with trip times of 145 and 168 days are presented. Effects due to variations in the trip time, departure and arrival orbit inclinations, initial fuel mass, and power level are investigated.