This research studies the potential of frozen low lunar orbits to be used in the design of constellations for global and regional communication or navigation. We introduce a robust two-stage approach to the frozen low lunar orbit design based on the successive application of non-gradient techniques, the Bayesian optimization and the Nelder–Mead method. The developed methodology has a number of advantages over existing numerical design techniques and allows revealing orbits with the periodic behavior of the eccentricity vector over long propagation intervals in the full dynamical model. By leveraging a convenient nomogram with constellation visibility parameters and lower bound coverage curves, we have identified most suitable low-altitude orbital configurations of Walker type and then adjust them to be frozen. The frozenness condition can be achieved without changing the orientation of orbital planes. Visibility and coverage metrics (multiplicity of continuous coverage for specified sites, polar regions, or the whole lunar surface; position dilution of precision) of candidate constellations are analyzed. Several promising designs of frozen constellations in near-circular low lunar orbits are singled out. The frozen orbit stability and the station-keeping cost are discussed.

This study is devoted to searching for lunar orbits that are accessible during departure along an unstable invariant manifold of halo orbits around lunar libration points L₁ and L₂. The spacecraft is assumed to be equipped with a low-thrust engine. Two levels of jet acceleration from the typical range of small-size spacecraft with low-thrust engines are considered. The study consists of two parts: (1) searching for osculating lunar orbits obtained during passive motion from halo orbits and (2) stabilization of orbits by the thrust force, directed against the spacecraft velocity. Many halo-orbits were found, the descent from which along the unstable manifold makes it possible to reach polar and near-polar orbits. The problem is solved within the model of a circular, restricted three-body problem.

This research presents a geometric analysis of Sun-assisted low-energy lunar transfers and several convenient tools that enable the systematic trajectory design in the framework of the planar bicircular restricted four-body problem. By analogy with the patched conic approximation approach for high-energy transfers, a Sun-assisted low-energy trajectory is divided into three legs. Two interior legs, departing and arriving, are located inside the Earth–Moon region of prevalence and designed in the Earth–Moon circular restricted three-body problem, whereas the exterior leg lies outside the region of prevalence and is calculated in the Earth–Moon–Sun bicircular restricted four-body model. The whole trajectory is obtained by smoothly patching the three legs on the boundary of the region of prevalence. The arrival conditions are met by targeting a specific point in the L₂ lunar gateway. The interior legs are easily adjustable to the four-body dynamics. The database of planar lunar transfer trajectories can be used to select an initial guess for the multiple-shooting procedure of designing a three-dimensional Sun-assisted lunar transfer in high-fidelity dynamical models.