Assessment of launch vehicle advances to enable human mars excursions

Abstract

A mathematical model is developed for the assessment of the launch mass of a vehicle designed for a human mission to Mars. The mission involves six stages: (i) ascent from Earth surface to low Earth orbit, (ii) outgoing trip from low Earth orbit to low Mars orbit, (iii) descent and landing on Mars, (iv) ascent from Mars surface to low Mars orbit, (v) return trip from low Mars orbit to low Earth orbit, (vi) descent and landing on Earth. The basic objective is to minimize the launch mass while containing the total flight time. The mathematical model includes two parts: interplanetary flight and planetary flight. The interplanetary flight model is based on the restricted four-body scheme and covers the spacecraft transfer from a low Earth orbit to a low Mars orbit and back. The planetary flight model concerns the spacecraft ascent from Earth surface to low Earth orbit and from Mars surface to low Mars orbit. The sequential gradient-restoration algorithm is employed to solve optimal trajectory problems of interplanetary flight in mathematical programming format and optimal trajectory problems of planetary flight in optimal control format. The planetary flight study shows that, due to the large gravitational constant of Earth, it is best to assemble the spacecraft in low Earth orbit and launch it from there, rather than from the Earth surface. To reduce the ratio of outgoing LEO mass to return LEO mass, it is best to design the spacecraft as consisting of three modules: Earth return module, habitation module, Mars excursion module. The interplanetary flight study shows that, for minimum energy LEO–LMO–LEO transfer, the total characteristic velocity is 11.30 km/ s . The round-trip time is 970 days, including a stay of 454 days on Mars while waiting for an optimal return date. For a fast transfer mission with a stay of 30 days on Mars, the round-trip time can be reduced to less than half at the cost of nearly doubling the characteristic velocity, thereby resulting into a mass ratio 10 times higher than that of a minimum energy mission, if chemical propellants are used. To decrease the total mass ratio, use of advanced techniques is indispensable. First, aerobraking techniques can contribute considerably to the reduction of mass ratios: excess velocity on arrival to Mars (outgoing trip) and excess velocity on arrival to Earth (return trip) can be depleted via aerobraking maneuvers instead of propulsive maneuvers. Second, the development of engine/propellant combinations with high specific impulse can be another key factor for reducing the mass ratio. Third, cargo transportation can be used: equipment and propellant not required for the outgoing trip can be sent before the crew leaves Earth via a cargo spacecraft using a low-thrust engine having high specific impulse. Numerical computation shows that, if both aerobraking techniques and cargo transportation techniques are employed, the mass ratio for a minimum energy mission can be brought down by a factor of 5, while the mass ratio for a fast transfer mission can be brought down by a factor of 20. To sum up, the mathematical model developed for a launch vehicle can help the engineer to assess proper development directions. Numerical results are highly dependent on certain factors characterizing hardware and propellant such as engine specific impulse, spacecraft structural factor, and aerobraking structural factor. At this time, we must look at a round trip Earth–Mars–Earth by humans as a formidable undertaking. This paper merely indicates some useful directions.