Fundamental issues of orbital transfers for Mars missions

Abstract

To assess the fundamental issues of orbital transfers for Mars missions, in particular, the interplay between flight time, characteristic velocity, and mass ratio, we study optimal round-trip LEO-LMO-LEO trajectories for a variety of boundary conditions, with LEO denoting a low Earth orbit and LMO denoting a low Mars orbit. In all cases, the criterion of optimization is the minimization of the characteristic velocity, which is the sum of all the velocity impulses; the optimization problems are solved via the sequential gradient-restoration algorithm in mathematical programming format. The assumed physical model is the restricted four-body model, the four bodies being the Sun, Earth, Mars, spacecraft. The round-trip trajectories considered differ from one another in the boundary conditions, specifically: (T1) stay time in LMO free, total time free, phase angle travel free, (T2) stay time in LMO of 30 days, total time free, phase angle travel free, (T3) stay time in LMO of 30 days, total time free, phase angle travel of the spacecraft equal to that of Earth, (T4) stay time in LMO of 30 days, total time of 440 days, phase angle travel of the spacecraft equal to that of Earth, (T5) zero stay time in LMO, total time free, phase angle travel free. Trajectories T1–T4 involve the circularization of the motion into LMO, Trajectory T5 is a free return trajectory with a Mars flyby. In the group of trajectories circularizing the motion into LMO, Trajectory T1 is a minimum energy trajectory, Trajectory T2 is a compromise trajectory, Trajectories T3 and T4 are fast transfer trajectories. From computation and analysis, the main results are as follows. (i) For a robotic spacecraft, the best trajectory is the minimum energy Trajectory T1, characterized by a flight time of 970 days, a characteristic velocity of 11.30 km/ s , and a mass ratio of 20. (ii) For a manned spacecraft, a substantial shortening of the flight time is needed, but this translates into stiff penalties in characteristic velocity and mass ratio. Indeed, for Trajectory T2, the flight time is 842 days, while the characteristic velocity is 15.61 km/ s and the mass ratio is 69; for Trajectory T3, the flight time is 546 days, while the characteristic velocity is 18.52 km/ s and the mass ratio is 150; for Trajectory T4, the flight time is 440 days, while the characteristic velocity is 20.79 km/ s and the mass ratio is 304. (iii) The free return Trajectory T5 is of no interest for Mars missions. While its characteristic velocity is nearly the same as that of Trajectory T1, the flight time has increased to 1214 days and the mass ratio has increased to 31. It must be noted that the above mass ratios refer to a round-trip LEO- LMO-LEO and do not include the ascent from/descent to the Earth surface (mass ratio of about 18) and the descent to/ascent from the Mars surface (mass ratio of about 3.6). When the above mass ratios are included, one obtains overall mass ratios of order 1000 for Earth–Mars–Earth transfer via a minimum energy trajectory and of order 10 000 for Earth–Mars–Earth transfer via a fast transfer trajectory. At the national level, the wisest strategy appears to be to continue the exploration of Mars via robotic spacecraft and delay the exploration of Mars via manned spacecraft to such time when, thanks to advances yet to be achieved in the areas of spacecraft structural factors and engine specific impulses, more reasonable values can be achieved for the characteristic velocity components and the mass ratio components.