2019/09/25 by Ioannis Gkolias, Jerome Daquin, Despoina K. Skoulidou +2 · 2 citations
Physics and Astronomy · Mathematics · #astro-ph.EP #math.DS #nlin.CD #physics.space-ph
paper · pdf · doi:10.1063/1.5124682
Accepted for publication in Chaos: An Interdisciplinary Journal of Nonlinear Science
arxiv created 2019/09/25 · arxiv updated 2019/10/28
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) ∼ t-α, with α∼ 0.8 - 1.5. Our study is highly relevant for the design of satellite disposal trajectories, using manifold dynamics.