Design and optimization of low-thrust orbital phasing maneuver

The minimum-time orbital phasing maneuver for a spacecraft with an electric thruster is studied. An efficient preliminary design method for phasing maneuver is developed. In this design method, two phasing strategies, an outward phasing strategy and an inward phasing strategy, are proposed based on the characteristics of the phasing mission. In the case of a circular orbit, an analytical solution is obtained by introducing certain assumptions. For the case of an elliptic orbit, a semi-analytical solution is obtained using the orbital averaging technique. Using this method, significant computational time can be saved because numerical integration of the long-duration phasing trajectory is avoided. In addition, the method is improved to design the phasing maneuver for the thrust-coast-thrust case. Furthermore, a shooting iteration method is adopted to improve the solution to satisfy the terminal constraints of high-precision numerical integration. The validity and accuracy of the preliminary design method are investigated by designing a variety of phasing missions. The results lead to several major conclusions: (1) The exponent of the phasing time is linearly proportional to the exponent of the thrust acceleration; (2) For the thrust-coast-thrust case, the total phasing time increases as the coast time increases, while the thrust time decreases; (3) The proposed preliminary design method can rapidly provide good initial guesses for the phasing maneuver optimization, and the shooting iteration method converges steadily and rapidly.