Chaotic transport of navigation satellites

TL;DR

This paper analytically investigates the chaotic dynamics of navigation satellites near circular orbits, revealing how hyperbolic invariant manifolds influence escape times and implications for satellite disposal strategies.

Contribution

It derives the fundamental Hamiltonian for GNSS dynamics and analytically demonstrates the role of NHIMs and their manifolds in satellite escape behavior.

Findings

Chaotic transport follows a power-law escape time distribution.

Near-circular orbits are influenced by a Normally Hyperbolic Invariant Manifold.

Results inform satellite disposal trajectory design.

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.