A fast low-thrust trajectory design method based on Multi-Motion Synthesis

A novel Multi-Motion Synthesis technique is proposed in this study for fast and accurate computation of low-thrust trajectories. It decomposes the trajectory into three motions during a time interval: a simple conic arc due to the Sun gravity only, a constant acceleration motion due to the constant low-thrust, and a motion due to the variation of the Sun gravity caused by the low-thrust. The final state of an interval is obtained analytically by the synthesis of these three motions. Simulation shows that the computational time using the technique is only 13.72% of numerical integration. And the position and velocity errors are on the order of 10⁴ km and 1.0 m/s, respectively. Finally, the low-thrust trajectory design method based on Multi-Motion Synthesis is applied to two rendezvous missions starting from the Earth: one is to the near Earth asteroid 99942 Apophis, and the other to the Mars. Results fully validate the availability and efficiency of the method.