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.

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.

In this study, a dynamical model is developed to describe the secular evolution of navigation satellites under the geocentric reference frame with the Laplace orbit as the fundamental plane. The disturbing function, involving the effects of Earth's oblateness and lunisolar gravitational attraction, is averaged over the orbital periods of both the satellite and the perturbers. In the regions of medium-Earth orbits and geosynchronous orbits, there are varieties of lunisolar resonances for governing the secular dynamics of navigation satellites. Among these resonances, we are interested in the ones occurring at the critical inclinations as well as the lunar node resonances. For each resonance of interest, the resonant center and width are identified analytically. Finally, dynamical maps are compared with the analytical results.