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 .