Fuel-Optimal, Low-Thrust, Three-Dimensional Earth-Mars Trajectories

Abstract

Fuel-optimal three-dimensional trajectories from Earth to Mars for spacecraft powered by a low-thrust rocket with variable speciŽ c impulse capability are presented. 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 is divided into segments, each deŽ ned with respect to a different central body. These segments are patched at intermediate time points, with proper matching conditions on the states and costates. The optimization problem is solved using an indirect multiple shootingmethod. Details of trajectories for 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 investigated.