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

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