Optimization of Low-Thrust Capture and Escape Trajectories

Abstract

During the last years Electric Propulsion (EP) has proven to be a viable option for the Solar System exploration, as it can improve the performance of probes and their scientific yield. The lower propellant consumption, compared to traditional chemical motors, and the possibility of achieving continuous steering capabilities, related to the long use of electric engines, make this propulsion technology very attractive for interplanetary trajectories. Even when EP is used for the interplanetary leg, Chemical Propulsion (CP) is usually employed to leave the Earth’s sphere of influence upon departure, as in the case of the Deep Space 1 mission 1 and the upcoming DAWN mission. 2 EP has instead been proposed to perform the capture at Mars arrival for a sample return mission. 3 The benefit of using the same high-specific-impulse EP system to perform different mission legs is obvious, at least if the longer trip time can be tolerated. Two potential applications of EP are considered in the present paper: the Earth-capture of a spacecraft that returns from an interplanetary mission, and the Earth-escape maneuver. Results can easily be extended to trajectories around other planets. The optimization of this kind of missions is obtained by means of a numerical procedure, which is based on an indirect approach, i.e., the theory of optimal control. The two-body problem formulation is considered to be sufficient for the preliminary analysis of this mission and, in particular, the patched conic approximation can be adopted; therefore, only the maneuver inside the Earth’s sphere of influence is considered in the present paper. The attention is here focused on the capture maneuver, but the extension to the escape case is straightforward. The strategies, which minimize the total propellant mass required for the low-thrust transfer from the edge of the terrestrial sphere of influence to the desired low Earth orbit (LEO), are sought when the approaching velocity is assigned. The trajectories are split into two parts. The approach phase, which can involve also ballistic arcs, is numerically optimized and inserts the spacecraft into a high circular orbit. The spiral phase brings the probe to the final LEO and is analyzed by adopting Edelbaum’s approximation 4 (i.e., an almost circular trajectory is considered). The junction point between these parts is optimized to maximize the spacecraft final mass, thus minimizing the total propellant mass. For the sake of simplicity the analysis starts from the two-dimensional problem and, in particular, from the comparison with another paper, 5 where Kluever presented a similar approach for the optimization of Earth-capture trajectories. The differences in the statement of the problem and results are motivated and explained. Several strategies, which involve also coast arcs, are examined as well as the influence of some parameters (namely, the thrust, the specific impulse, and the initial velocity of the spacecraft). Threedimensional capture trajectories are then presented and compared with the results of the two-dimensional problem. Escape maneuvers are finally considered.