Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios

Valk, S.; Lemaître, Anne; Anselmo, Luciano

doi:10.1016/j.asr.2007.10.025

Cited by 53 publications

(63 citation statements)

References 5 publications

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“…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.…”

Section: Dynamics Of Large Area-to-mass Ratio Objectsmentioning

confidence: 99%

A study of the main resonances outside the geostationary ring

Celletti

Galeş

2015

Advances in Space Research

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Abstract. We investigate the dynamics of satellites and space debris in external resonances, namely in the region outside the geostationary ring. Precisely, we focus on the 1:2, 1:3, 2:3 resonances, which are located at about 66 931.4 km, 87 705.0 km, 55 250.7 km, respectively. Some of these resonances have been already exploited in space missions, like XMM-Newton and Integral.Our study is mainly based on a Hamiltonian approach, which allows us to get fast and reliable information on the dynamics in the resonant regions. Significative results are obtained even by considering just the effect of the geopotential in the Hamiltonian formulation. For objects (typically space debris) with high area-to-mass ratio the Hamiltonian includes also the effect of the solar radiation pressure. In addition, we perform a comparison with the numerical integration in Cartesian variables, including the geopotential, the gravitational attraction of Sun and Moon, and the solar radiation pressure.We implement some simple mathematical tools that allows us to get information on the terms which are dominant in the Fourier series expansion of the Hamiltonian around a given resonance, on the amplitude of the resonant islands and on the location of the equilibrium points. We also compute the Fast Lyapunov Indicators, which provide a cartography of the resonant regions, yielding the main dynamical features associated to the external resonances. We apply these techniques to analyze the 1:2, 1:3, 2:3 resonances; we consider also the case of objects with large area-to-mass ratio and we provide an application to the case studies given by XMM-Newton and Integral.

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Section: Dynamics Of Large Area-to-mass Ratio Objectsmentioning

confidence: 99%

A study of the main resonances outside the geostationary ring

Celletti

Galeş

2015

Advances in Space Research

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“…We start with a short description of the semi-analytical theory; for more details we refer the reader to Valk et al (2008Valk et al ( , 2009b. The framework is a mean motion semi-analytical theory: only the long-term and secular effects are derived.…”

Section: Valk Semi-analytical Studymentioning

confidence: 99%

“…As a second validation of our software, we applied NIMASTEP to the typical case of an high-altitude abandoned space debris and compared our results with two semi-analytical theories: the STELA software and a semi-analytical study of Valk et al (2008Valk et al ( , 2009b.…”

Section: Comparisons With Semi-analytical Theoriesmentioning

confidence: 99%

“…Valk et al (2008Valk et al ( , 2009b expanded the Earth potential in powers of the eccentricity and of the inclination, truncated the development at a low order to obtain an Hamiltonian formulation. Some other perturbations were added, such as the direct radiation pressure ) and the solar and lunar gravitational effects.…”

Section: Valk Semi-analytical Studymentioning

confidence: 99%

“…The integration time is equal to 100 years. The entry-level step size used in the osculating numerical integration with NIMASTEP is fixed at 200 s (with the RK4 method), whereas Valk et al (2008) define a one day step size to integrate the averaged system of equations (also with the RK4 method).…”

Section: Valk Semi-analytical Studymentioning

confidence: 99%

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

Delsate

Compère

2012

A&A

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NIMASTEP is a dedicated numerical software developed by us, which allows one to integrate the osculating motion (using Cartesian coordinates) in a Newtonian approach of an object considered as a point-mass orbiting a homogeneous central body that rotates with a constant rate around its axis of smallest inertia. The code can be applied to objects such as particles, artificial or natural satellites, or space debris. The central body can be either any terrestrial planet of the solar system, any dwarf-planet, or even an asteroid. In addition, very many perturbations can be taken into account, such as the combined third-body attraction of the Sun, the Moon, or the planets, the direct solar radiation pressure (with the central body shadow), the non-homogeneous gravitational field caused by the non-sphericity of the central body, and even some thrust forces. The simulations were performed using different integration algorithms. Two additional tools were integrated in the software package; the indicator of chaos MEGNO and the frequency analysis NAFF. NIMASTEP is designed in a flexible modular style and allows one to (de)select very many options without compromising the performance. It also allows one to easily add other possibilities of use. The code has been validated through several tests such as comparisons with numerical integrations made with other softwares or with semi-analytical and analytical studies. The various possibilities of NIMASTEP are described and explained and some tests of astrophysical interest are presented. At present, the code is proprietary but it will be released for use by the community in the near future. Information for contacting its authors and (in the near future) for obtaining the software are available on the web site http://www.fundp.ac.be/en/research/projects/ page_view/10278201/

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Space Debris: From LEO to GEO

Lemaître

2019

Satellite Dynamics and Space Missions

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Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios

Cited by 53 publications

References 5 publications

A study of the main resonances outside the geostationary ring

A study of the main resonances outside the geostationary ring

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

Space Debris: From LEO to GEO

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