Orbits that are frozen in an averaged model, including the effect of a disturbing body laying on the equatorial plane of the primary body and the influence of the oblateness of the primary body, have been applied to probes orbiting the Moon. In this scenario, the main disturbing body is represented by the Earth, which is characterized by a certain obliquity with respect to the equatorial plane of the Moon. As a consequence of this, and of the perturbing effects that are not included in the averaged model, such solutions are not perfectly frozen. However, the orbit eccentricity, inclination, and argument of pericenter present limited variations and can be set to guarantee the fulfillment of requirements useful for lunar telecommunication missions and navigation services. Taking advantage of this, a practical case of a Moon-based mission was investigated to propose useful solutions for potential near-future applications.

This article studies the problem of analyzing the coverage capacity of satellite constellations with respect to ground regions. The coverage characteristics and formulations are first investigated, and a corresponding symbol system is established. On this basis, the coverage state function and the corresponding extension and intermediate modes for basic coverage analysis problems are defined. By introducing the parameter wildcard characters, the properties of three basic spatial and temporal factors are described. An integrated coverage theory system is constructed accordingly to formalize the general coverage analysis problems in a uniform way, which is versatile and works on representing any type of coverage analysis problems. Additionally, in accordance with the properties of the coverage theory, a boundary function is proposed. The corresponding algorithm framework is also constructed for the calculation of complicated practical coverage analysis problems. Experiments simulating different types of coverage analysis problems are carried out, and results reveal the correctness and the effectiveness of the proposed coverage theory system and algorithm framework.

The dynamics of a probe orbiting a moon can be significantly influenced by the non-coincidence between the moon’s equatorial and orbital planes. Thus, we performed a general analysis about the effects of the angle (obliquity) between the above-mentioned planes and of the angle (nodal phasing) between the nodal lines of the mother planet’s apparent orbit and the probe orbit on the lifetime of the probe. The lifetime, strictly correlated to the variations in eccentricity of the probe orbit, was evaluated starting from low values of the semi-major axis, moderate eccentricity, and high inclination to offer high ground spatial resolution and extend latitudinal coverage of the natural satellite. This investigation, carried out through numerical simulations, may be useful for identifying the optimal initial conditions of the probe’s orbit elements, leading to an important increase in the probe lifetime in missions devoted to the exploration of natural satellites.