High-fidelity dynamics modeling of long-term station keeping around Earth-Moon synodic resonant halo orbits using solar sails

Halo orbits in the Earth-Moon system are useful for many applications related to lunar exploration. Because they are generally unstable, station-keeping control is required for a spacecraft to prevent orbital escape. Solar sails are a propulsion system that produces thrust without consuming propellant. Although the magnitude of thrust is small, they are suitable for long-term station keeping around halo orbits. Because the direction of the Sun rotates in the Earth-Moon rotating frame, halo orbits around the Earth-Moon libration points must be synodic resonant to retain periodicity, where the ratio of the orbital periods to the synodic lunar period is rational. In this study, a long-term (e.g., more than 1 year) orbit design method in the high-fidelity ephemeris model was first developed. To make it possible, a successive orbit design method was devised, wherein relatively short-term orbits are sequentially designed such that they are connected to each other smoothly to retain the synodic resonance geometry. Simulation results indicated that it can be applied to at least around 2-year synodic resonant halo orbits. In addition, a station-keeping strategy to stay near the reference orbits under the influence of navigation error and attitude control error was developed. It was formulated using the state transition matrix and its Cauchy-Green tensor to minimize the future position and velocity error with respect to the reference orbit. The simulation results showed how the performance of the method changes according to the parameters (e.g., sail area-to-mass ratio, nominal Sun angle, and guidance and control frequency).