The presented work examines frozen and quasi-frozen lunar orbits as a possible basis for low-altitude satellite communication and navigation systems around the Moon. Numerical simulations were performed using a high-fidelity dynamic motion model, incorporating the gravitational field of the Moon (LP165), gravitational perturbations from the Earth and the Sun, and solar radiation pressure. Orbits with altitudes between 200 and 400 km and inclinations from 0° to 90° are considered.

Based on a series of 349 numerical experiments, a catalog of frozen and quasi-frozen orbital configurations was compiled, classified by altitude, inclination, eccentricity, and orbital orientation. It is shown that frozen orbits within the studied parameter range exist only for certain combinations of altitude and inclination, primarily in the near-polar region, while stable quasi-frozen regimes are realized over broader, but also limited, parameter ranges. The resulting solutions were additionally tested for long-term stability over intervals of up to ten years.

For a number of typical cases, the numerical simulation results were compared to a semi-analytical solutions obtained using an averaged motion model (the SELENA - SEmi-anaLytical IntEgrator for a luNar Artificial satellite- method proposed by the University of Padova (UniPd), and the Aristotle University of Thessaloniki (AUTH)). Qualitative agreement was demonstrated in the localization of frozen and quasi-frozen orbits, confirming the validity of the identified patterns and stable orbital configurations.

It was established that the altitude range of approximately 300–350 km, where the greatest number of stable frozen and quasi-frozen orbital configurations is observed , can be considered as the most favorable region for constructing low-lunar satellite systems . The influence of the argument of latitude and the right ascension of ascending node (RAAN) on the preservation of frozen properties have been studied.

The resulting orbit catalog was used in the design of low-lunar satellite constellations for the LunarCubeNet system. Various constellation architectures were compared based on three criteria: lunar surface coverage, continuity of Earth-Moon communication, and the proportion of satellites deployed in frozen and quasi-frozen orbits. Based on the conducted analysis, preferred configurations of low-lunar relay systems for promising lunar missions were determined.