On the role of the fast oscillations in the secular dynamics of the lunar coplanar perturbation on Galileo satellites

TL;DR

This paper explores how lunar fast oscillations influence the secular dynamics of Galileo satellites, revealing differences between simplified models and full system behavior, with implications for natural orbit decay mechanisms.

Contribution

It provides a detailed comparison of secular Hamiltonian dynamics and full system periodic orbits, highlighting the impact of lunar oscillations on satellite stability.

Findings

Differences depend on the ratio of satellite and Moon semi-major axes.

Fast oscillations significantly affect the stability of satellite orbits.

Results inform the understanding of natural orbit decay via Arnold diffusion.

Abstract

Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability of the fixed points associated with the secular Hamiltonian averaged with respect to the fast variable with the corresponding periodic orbits of the full system. Focusing on the orbit of the Galileo satellites, it turns out that the two dynamics cannot be confused, as the relative difference depends on the ratio between the semi-major axis of Galileo and the one of the Moon, that is not negligible. The result is relevant to construct rigorously the Arnold diffusion mechanism that can drive a natural growth in eccentricity that allows a satellite initially on a circular orbit in Medium Earth Orbit to reenter into the Earth's atmosphere.