Chaos in navigation satellite orbits caused by the perturbed motion of the Moon

TL;DR

This paper demonstrates that the chaotic behavior of navigation satellite orbits is caused by overlapping secular resonances involving lunar motion, revealing a complex stochastic web in phase space similar to other celestial bodies.

Contribution

It uncovers the resonance mechanisms behind satellite orbit chaos, linking it to lunar-induced secular resonances and phase space web structures.

Findings

Satellite orbits exhibit chaotic growth of eccentricity.

Resonance overlap leads to chaos in orbital dynamics.

Lunar secular resonances influence satellite orbit stability.

Abstract

Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here we show that the irregular and haphazard character of these orbits reflects a similar irregularity in the orbits of many celestial bodies in our Solar System. We find that secular resonances, involving linear combinations of the frequencies of nodal and apsidal precession and the rate of regression of lunar nodes, occur in profusion so that the phase space is threaded by a devious stochastic web. As in all cases in the Solar System, chaos ensues where resonances overlap. These results may be significant for the analysis of disposal strategies for the four constellations in this precarious region of space.