This paper deals with the optimal design of round-trip Mars missions, starting from LEO (low Earth orbit), arriving to LMO (low Mars orbit), and then returning to LEO after a waiting time in LMO.

The assumed physical model is the restricted four-body model, including Sun, Earth, Mars, and spacecraft. The optimization problem is formulated as a mathematical programming problem: the total characteristic velocity (the sum of the velocity impulses at LEO and LMO) is minimized, subject to the system equations and boundary conditions of the restricted four-body model. The mathematical programming problem is solved via the sequential gradient-restoration algorithm employed in conjunction with a variable-stepsize integration technique to overcome the numerical difficulties due to large changes in the gravity field near Earth and near Mars.

The results lead to a baseline optimal trajectory computed under the assumption that the Earth and Mars orbits around Sun are circular and coplanar. The baseline optimal trajectory resembles a Hohmann transfer trajectory, but is not a Hohmann transfer trajectory, owing to the disturbing influence exerted by Earth/Mars on the terminal branches of the trajectory. For the baseline optimal trajectory, the total characteristic velocity of a round-trip Mars mission is 11.30 km/s (5.65 km/s each way) and the total mission time is 970 days (258 days each way...