Orbit transfer optimization for lunar relay satellite with electric thrust based on Q-law

Due to the relative position invariance of L2 Libration point in the Earth-moon system, Halo orbits around LL2 adapt to the best mission trajectory for Lunar Relay Satellite, which can offer relay communication for space missions such as deep-space exploration and Moon outpost construction. In order to improve the payload launch capacity of Lunar Relay Satellite, the electric thrusters which have high specific impulse and low thrust can be used as main propulsion. In this paper, the Q-law control theory in optimal control theory is adopted to calculate the optimal transfer orbit of Lunar Relay Satellite using electric thrusters. In addition, the effect of initial orbit of transfer trajectory and invariant manifold has been considerate. The result shows the design rules and the algorithm is of great important engineering meaning.