  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.
