Long-term frozen repeat orbits with large eccentricity under complex perturbations

Highly-elliptical frozen repeat orbits have emerged as the optimal choice for high-latitude lunar missions due to their stable orbits and ability to repeatedly cover the same areas. However, in addition to the (Formula presented) perturbation, lunar orbits are also significantly influenced by the (Formula presented) and third-body perturbations, which cause more pronounced periodic drifts to orbital elements, posing substantial challenges to maintaining the frozen and repeat properties. To address this challenge, a relevant methodology has been proposed, which achieves simultaneous correction of orbital repeat property and preservation of the frozen property through a single numerical adjustment. It effectively eliminates the computational burden of iterative adjustments required by conventional methods. By adjusting the semi-major axis, eccentricity, and inclination of the orbit, the drift of sub-satellite point trajectory and eccentricity vector caused by unmodeled perturbations is constrained, where the sub-satellite point drift is defined as the longitude difference between consecutive ascending nodes after a repeat cycle. Simulation results demonstrate that the proposed method enables the design of orbits with long-term, high-precision revisits and fixed perilune. This provides a novel, robust, and feasible orbital design concept for lunar exploration missions in complex perturbation environments.