Fuel-optimal Earth-Mars trajectories using low-thrust exhaust-modulated plasma propulsion

Abstract

The objective of this thesis is the determination of fuel-optimal interplanetary trajectories of a spacecraft using a variable specific impulse thruster. The spacecraft departs from an Earth parking orbit and is required to establish a specified orbit about Mars within a fixed time frame. The trajectory and spacecraft parameters have been chosen to simulate the outbound leg of a planned human mission to Mars in the year of 2014. The optimizations involve both planar and three-dimensional trajectories. To avoid numerical sensitivity, the entire Earth-Mars trajectory is divided into segments with different reference frames. An indirect, multiple-shooting method is utilized to solve the optimal control problem. Due to the need for a good set of initial guesses, the trajectories are determined in a series of steps. The procedure is initiated by solving subproblems that involve only single segments. Upon obtaining solutions to the subproblems, the individual segments are patched together to generate a complete trajectory. The planar problem is considered first. It allows preliminary analyses and an examination of the problem sensitivity. Besides, the planar results provide a rough estimation of the "optimal'' departure date for the mission. The problem is extended into three-dimensional space after the planar trajectory study. With an extra degree of freedom, various departure and arrival parking orbit inclinations can be specified. It is found that, for the departure date considered, a trajectory with a lower cost can be achieved if a near-polar capture orbit is enforced. The effect of the flight time on the performance index is also investigated. The analysis reveals that increasing the mission duration from 145 days, as originally specified, to 168 days reduces the fuel consumption by 6.12%. The results of the determined trajectories reveal exploitations of the thrust modulation capability of the plasma engine. The modulations are evident in the heliocentric transfer arc and Mars-entry phase of the trajectories. A constant thrust level, on the other hand, is maintained during most of the Earth-escape phase. However, for some trajectories, particularly those with a trip-time of 150 days or longer, rapid thrust modulations are observed in the escape phase.