Chaotic transport of navigation satellites

Abstract

Navigation satellites are known from numerical studies to reside in a dynamically sensitive environment, which may be of profound importance for their long-term sustainability. We derive the fundamental Hamiltonian of GNSS dynamics and show analytically that near-circular trajectories lie in the neighborhood of a Normally Hyperbolic Invariant Manifold (NHIM), which is the primary source of hyperbolicity. Quasi-circular orbits escape through chaotic transport, regulated by the NHIM's stable and unstable manifolds, following a power-law escape time distribution $P(t)\sim t^{-\alpha }$, with $\alpha \sim 0.8-1.5$. Our study is highly relevant for the design of satellite disposal trajectories, using manifold dynamics.

arXiv commentAccepted for publication in Chaos: An Interdisciplinary Journal of Nonlinear Science

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Cited by in corpus (3)

• A deep dive into the $2g+h$ resonance: separatrices, manifolds and phase space structure of navigation satellites
• Dynamical properties of the Molniya satellite constellation: long-term evolution of orbital eccentricity
• Partial barriers to chaotic transport in 4D symplectic maps