From order to chaos in Earth satellite orbits

TL;DR

This paper investigates the long-term dynamical behavior of Earth satellite orbits in MEO and GEO, revealing a transition from order to chaos influenced by secular resonances and inclination, with implications for space debris management.

Contribution

It applies a Hamiltonian model and chaos indicators to characterize the transition to chaos in satellite orbits, especially near secular resonances, using a novel statistical approach with FLI maps.

Findings

Transition from order to chaos near critical inclinations

Highly inclined GEO orbits are particularly unstable

Rich dynamical behaviors observed in satellite orbits

Abstract

We consider Earth satellite orbits in the range of semi-major axes where the perturbing effects of Earth's oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of first importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations, and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.