Long-Term Station Keeping of Frozen Orbits Based on Averaged Dynamics

This paper proposes a low-thrust strategy for the station keeping of unstable frozen orbits around planetary moons, which aims to keep the orbital evolution near unstable frozen orbits in the long-term sense. The strategy is based on the potential shaping. An artificial modification to the doubly averaged perturbing potential is designed to stabilize the orbital motion in the vicinity of the unstable frozen orbits. To achieve effects of the artificial potential modification, a method for computing equivalent control thrust accelerations is developed. The thrust accelerations are expressed as trigonometric functions of the true anomaly, and their long-term effects on orbital evolution are designed to be equivalent to the potential modification by using averaging. The effectiveness of the proposed strategy is validated through its application to the station keeping of high-inclination unstable frozen orbits around Europa. Results indicate that the strategy can successfully confine the orbital evolution to the vicinity of the unstable frozen orbits, with the required ΔV cost of approximately 0.2∼0.3 m/s per day. The maximum deviations during the station keeping are quite small, even in the presence of initial insertion errors.