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

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.

5 pages, 3 figures; accepted for publication in MNRAS

References in corpus (1)

• On the dynamics of space debris: 1:1 and 2:1 resonances

Cited by in corpus (11)

• Dynamical cartography of Earth satellite orbits
• Geostationary secular dynamics revisited: application to high area-to-mass ratio objects
• A deep dive into the $2g+h$ resonance: separatrices, manifolds and phase space structure of navigation satellites
• Towards a sustainable exploitation of the geosynchronous orbital region
• Dynamical properties of the Molniya satellite constellation: long-term evolution of orbital eccentricity
• Medium Earth Orbit dynamical survey and its use in passive debris removal
• Chaotic transport of navigation satellites
• Dynamical Lifetime Survey of Geostationary Transfer Orbits
• The Precise and Powerful Chaos of the 5:2 Mean Motion Resonance with Jupiter
• Efficient trajectory design for distant planetary orbiters
• Asymptotic behaviour of orbit determination for hyperbolic maps