Influence of Earth’s shadowing effects on space debris stability

• Published in: Advances in space research Vol. 51; no. 1; pp. 25 - 38
• Main Authors: Hubaux, Ch, Libert, A.-S., Delsate, N., Carletti, T.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.01.2013; Elsevier
• Subjects: Astronomy; Astrophysics; Detection of chaos; Earth, ocean, space; Exact sciences and technology; External geophysics; Physics; Shadowing effects; Solar radiation pressure; Space debris; Symplectic integration; Symplectic integration; Detection of chaos; Space debris; Solar radiation pressure; Shadowing effects; Chaos; Short term; Growth; Shading; Orbits; Equations of motion; Space research; Long term; Radiation pressure; Variational equation; Hamiltonians; Orbit stability; Propagator; Models; Diffusion; Performance; Solar radiation; Altitude
• ISSN: 0273-1177; 1879-1948
• DOI: 10.1016/j.asr.2012.08.011

► We show that Earth’s shadows make chaotic the geostationary orbit of space debris with high area-to-mass ratios. ► We compare adapted conical and cylindrical Earth’s shadowing models. ► We symplectically integrate both Hamiltonian equations of motion and variational equations. ► We propose a new method to compute efficiently the Mean Exponential Growth factor of Nearby Orbits criterion. ► We discuss the choice of symplectic integration scheme. Solar radiation pressure affects the evolution of high area-to-mass geostationary space debris. In this work, we extend the stability study of Valk et al. (2009) by considering the influence of Earth’s shadows on the short- and long-term time evolutions of space debris. To assess the orbits stability, we use the Mean Exponential Growth factor of Nearby Orbits (MEGNO), which is an efficient numerical tool to distinguish between regular and chaotic behaviors. To reliably compute long-term space debris motion, we resort to the Global Symplectic Integrator (GSI) of Libert et al. (2011) which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. We show how to efficiently compute the MEGNO indicator in a complete symplectic framework, and we also discuss the choice of a symplectic integrator, since propagators adapted to the structure of the Hamiltonian equations of motion are not necessarily suited for the associated variational equations. The performances of our method are illustrated and validated through the study of the Arnold diffusion problem. We then analyze the effects of Earth’s shadows, using the adapted conical and cylindrical Earth’s shadowing models introduced by Hubaux et al. (2012) as the smooth shadow function deriving from these models can be easily included into the variational equations. Our stability study shows that Earth’s shadows greatly affect the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude. We also emphasize the differences in the results given by conical or cylindrical Earth’s shadowing models. Finally, such results are compared with a non-symplectic integration scheme.