2016/06/30 by Ioannis Gkolias, Jérôme Daquin, Jerome Daquin +2 · 44 citations
Physics and Astronomy · #Astro and Planetary Science #Astronomy #Celestial mechanics #Classical mechanics #Geosynchronous orbit #Gravitation #Perturbation (astronomy) #Physics #Quantum chaos and dynamical systems #Satellite #Statistical physics #Stellar, planetary, and galactic studies #astro-ph.EP #nlin.CD
paper · pdf · doi:10.3847/0004-6256/152/5/119
published in The Astronomical Journal 152(5), 119 (Institute of Physics) · 30 pages, 9 figures. Accepted for publication in the Astronomical Journal
arxiv created 2016/10/13 · openalex publication_date 2016/10/14 · arxiv updated 2016/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
ABSTRACT We consider Earth satellite orbits in the range of semimajor 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 primary 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.