Trajectories for Human Missions to Mars, Part 2: Low-Thrust Transfers

We compute optimal low-thrust transfers (with constant thrust and constant specific impulse) between Earth and Mars over a range of flight times (from 120 to 270 days) and launch years (between 2009 and 2022). Unlike impulsive transfers, the mass-optimal trajectory depends strongly on the thrust and specific impulse of the propulsion system. A low-thrust version of the rocket equation is provided where the initial mass or thrust may be minimized by varying the initial acceleration and specific impulse for a given power-system specific mass and for a trajectory time of flight. With fixed time-of-flight transfers there is a minimum thrust and a maximum allowable specific mass; that is, if the available thrust is too low or the specific mass is too large then the desired transfer does not exist. We find the minimum allowable thrust for constrained time-of-flight missions is on the order of a few Newtons per metric ton of payload for power systems with tens of kg/kW. As expected, the thrust and AV requirements of the trajectories decrease with increasing flight times. By extending the flight time from 180 to 270 days the A V is reduced by 40% for powered captures and up to 35% for aeroassisted capture trajectories.