Chaotic transport of navigation satellites

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 Global Navigation Satellite System 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. Quasicircular orbits escape through chaotic transport, regulated by 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.