Design of elliptical lunar frozen orbits with high accuracy

Lunar telecommunication and navigation architectures can significantly benefit from placing probes in stable elliptical orbits. Building upon previous research that identified families of quasi-frozen solutions using a double-averaged model (accounting for lunar oblateness and the Earth’s third-body perturbation under a quadrupole approximation of the terrestrial potential), this study extends the analytical framework to the octupole level. The solutions are subsequently employed as initial guesses for a high-fidelity numerical investigation. This comprehensive model removes prior simplifying assumptions, incorporating the Moon’s full gravitational field alongside perturbations from both the Earth and the Sun. Ultimately, we demonstrate the robustness of these refined configurations, supporting their use in the design of future lunar mission architectures.