Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator

Abstract

In this paper we provide an extensive analysis of the global dynamics of high-areato-mass ratios geosynchronous (GEO) space debris, applying a recent technique developed by Cincotta and Simó (2000), Mean Exponential Growth factor of Nearby Orbits (MEGNO), which provides an efficient tool to investigate both regular and chaotic components of the phase space.We compute a stability atlas, for a large set of near-geosynchronous space debris, by numerically computing the MEGNO indicator, to provide an accurate understanding of the location of stable and unstable orbits as well as the timescale of their exponential divergence in case of chaotic motion. The results improve the analysis presented in Breiter et al. (2005) notably by considering the particular case of higharea-to-mass ratios space debris. The results indicate that chaotic orbits regions can be highly relevant, especially for very high area-to-mass ratios.We then provide some numerical investigations and an analytical theory that lead to a detailed understanding of the resonance structures appearing in the phase space. These analyses bring to the fore a relevant class of secondary resonances on both sides of the well-known pendulum-like pattern of geostationary objects, leading to a complex dynamics.

NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

“…To our knowledge, the first uses of NAFF in the geodesy context were published by , Delsate et al (2008) and Valk et al (2009a). In Valk et al (2009a), the authors (using NIMASTEP and NAFF) computed the frequency of the resonant angle of the geostationary orbit.…”

“…This indicator has been successfully used in some papers, for instance, Breiter et al (2005), Cincotta & Simó (2000), Goździewski et al (2001Goździewski et al ( , 2008 and Hinse et al (2008Hinse et al ( , 2010. For the results concerning the MEGNO implemented into NIMASTEP we refer the reader to Valk et al (2009a) and Compère et al (2012).…”

“…In Valk et al (2009a), the authors (using NIMASTEP and NAFF) computed the frequency of the resonant angle of the geostationary orbit. Their results agree well with the theory of Valk et al (2009b).…”

“…NIMASTEP has been (first) implemented during the Ph.D. thesis of N. Delsate (Delsate 2011b). NIMASTEP was initially developed to numerically integrate the motion of an artificial satellite orbiting a telluric planet (Delsate et al 2010;Valk et al 2009a) 1 . Later on this software was extended to calculate the motion of one or several artifical (Delsate 2011a) or natural satellites (Compère et al 2012) orbiting a (dwarf-)planet or an asteroid of the solar system.…”

A study of the main resonances outside the geostationary ring

“…Extended analyses of the dynamics of high area-to-mass ratio objects are provided in several papers (see, e.g., [4], [16], [17], [21], [22], [23]). The purpose of this section is to explore the interaction of such objects with the 1:2, 2:3, 1:3 resonances, by using the Hamiltonian formalism.…”