Although chemical rocket propulsion is widely used in space transportation, large amounts of propellant mass limit designs for spacecraft missions to Mars. Electrical propulsion, which requires a smaller propellant load, is an alternative propulsion system that can be used for interplanetary flight. After the recent successes of the NASA Deep Space 1 spacecraft and the ESA SMART 1 spacecraft, which incorporate an electrical propulsion system, there is a strong need for trajectory tools to support these systems.
This thesis describes the optimization of interplanetary trajectories from Earth to Mars for spacecraft utilizing low-thrust electrical propulsion systems. It is assumed that the controls are the thrust direction and the thrust setting. Specifically, the minimum time and minimum propellant problems are studied and solutions are computed with the sequential gradient-restoration algorithm (SGRA).
The results indicate that, when the thrust direction and thrust setting are simultaneously optimized, the minimum time and minimum propellant solutions are not identical. For minimum time, it is found that the thrust setting must be at the maximum value; also, the thrust direction has a normal component with a switch at midcourse from upward to downward. This changes the curvature of the trajectory, has a beneficial effect on time, but a detrimental effect on propellant mass; indeed, the propellant mass ratio of the minimum time solution is about twice that of the Hohmann transfer solution. Thus, the minimum time solution yields a rather inefficient trajectory. For minimum propellant consumption, it is found that the best thrust setting is bang-zero-bang (maximum thrust, followed by coasting, followed by maximum thrust) and that the best thrust direction is tangent to the trajectory. This is a rather efficient trajectory; to three significant digits, the associated mass ratio is the same as that of the Hohmann transfer solution, even for thrust-to-weight ratios of order 10-4.
For a robotic spacecraft, it is clear that the minimum propellant mass solution is to be preferred. For a manned spacecraft, the transfer time and propellant mass functionals have comparable importance; they are in conflict with one another for the following reason: any attempt at reducing the former increases the latter and viceversa. This suggests the construction of a compromise functional, which is the linear combination of the previous two functionals, suitably scaled. The compromise functional depends on a parameter C (compromise factor) in the range 0 ≤ C ≤ 1 and is such that it reduces to the transfer time functional for C = 0 and to the propellant mass functional for C = 1. (Abstract shortened by UMI.)