Mission opportunities for human exploration of Mars

Abstract

An indirect optimization procedure is applied to find the mission opportunities for a manned or round-trip mission to Mars. Both the conjunction-class and opposition-class high-thrust trajectories are considered, taking into account simple legs (with only departure and arrival impulses), three-impulse legs (departure, midcourse and arrival impulses) and flyby legs, where the non-propelled flyby of the planet Venus is used instead of the midcourse impulse to reduce the propellant consumption. The absolute positions of all the relevant planets repeat almost perfectly after 32 years: therefore, only the mission opportunities in a 32-year syzygistic cycle are analyzed. The two-body problem formulation is sufficient for preliminary analyses of interplanetary missions and the trajectory is approximated by heliocentric conic orbits passing through the centres of the planets. The mission opportunities correspond to the local minima of the characteristic velocity, that is, the sum of the actual velocity changes obtained by expending the propellant. Numerical results are presented to show that the same mathematical approach can be applied to different classes of missions, to emphasize the indications suggested by Pontryagin's Maximum Principle, to point out some periodicities in the solutions and to discuss the problem of providing initial guesses at the solutions.