From order to chaos in Earth 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.

30 pages, 9 figures. Accepted for publication in the Astronomical Journal

References in corpus (8)

• The Eccentric Kozai-Lidov Effect and Its Applications
• Suppression of extreme orbital evolution in triple systems with short range forces
• Satellite dynamics on the Laplace surface
• Chaos in navigation satellite orbits caused by the perturbed motion of the Moon
• Saturn's inner satellites : orbits, masses and the chaotic motion of Atlas from new Cassini imaging observations
• Stability of Distant Satellites of Giant Planets in the Solar System
• Exponential growth of eccentricity in secular theory
• Diffusive chaos in navigation satellites orbits

Cited by in corpus (16)

• Dynamical cartography of Earth satellite orbits
• Dynamical models and the onset of chaos in space debris
• Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods
• Towards a sustainable exploitation of the geosynchronous orbital region
• A deep dive into the $2g+h$ resonance: separatrices, manifolds and phase space structure of navigation satellites
• Medium Earth Orbit dynamical survey and its use in passive debris removal
• Chaotic transport of navigation satellites
• Dynamical Lifetime Survey of Geostationary Transfer Orbits
• Detection of separatrices and chaotic seas based on orbit amplitudes
• Drift and its mediation in terrestrial orbits
• On the predictability of Galileo disposal orbits
• Characterisation of chaos in meteoroid streams. Application to the Geminids
• Uncontrolled geostationary satellites: mapping periodic transitions to chaos with Lagrangian Descriptors
• Semi-analytical estimates for the orbital stability of Earth's satellites
• Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression
• A Rapid Method For Orbital Coverage Statistics With ${\mathbf{J}}_2$ Using Ergodic Theory