Abstract
Our lifestyle is strongly dependent on the presence of spacecraft: telecommunications, GPS or cellular phones, TV, Internet, climate watches, ecological studies, catastrophe prevention, military surveys,… Despite the technological progress, the costs and the risks due to the space debris are increasing and can really stop or drastically reduce the systematic replacement or extension of the present satellite constellations, stopping the worldwide communication.
In the next years, a special attention should be dedicated to the space debris problematic, to protect the space environment and to allow technological innovations, in the present framework of sustainable development.
In particular, more precise information about the dynamics and the behavior of debris has to be collected; the methods and theories of classical celestial mechanics are very suitable to describe the long term dynamics of these debris. Interesting results have been obtained by new approaches of the problem: the resonant description of the dynamics of geosynchronous debris, the consideration of the solar radiation pressure as an important perturbation, specially for objects with a large A/m coefficients and, because of the lifetimes of the debris, the use of symplectic integrators, as for the natural bodies but adapted to the specific force model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
1 The 2007 Chinese anti-satellite missile test was conducted by China on January 11, 2007. A Chinese weather satellite, the FY-1C polar orbit satellite of the Fengyun series, at an altitude of 865 kilometer with a mass of 750 kg was destroyed by a kinetic kill vehicle traveling with a speed of 8 km/s in the opposite direction.
- 2.
2 The collision occurred on February 10, 2009, at 789 kilometer above the Taymyr Peninsula in Siberia, when Iridium 33 and Kosmos 2251 collided at a speed of 11.7 kilometer per second. The Iridium satellite was an American telecommunication satellite member of a constellation, it was still operational at the time of the collision, while the Russian military satellite had been out of service since at least 1995 and was no longer actively controlled.
References
Aksnes, K.: Short-period and long-period perturbations of a spherical satellite due to direct solar radiation. Celestial Mechanics 13, 89–104 (1976)
Beutler, G.: Methods of celestial mechanics. Physical, mathematical, and numerical problems, Volumes 1 & 2. Springer-Verlag, Berlin Heidelberg (2005)
Breiter, S., Wytrzyszczak, I., Melendo, B.: Long-term predictability of orbits around the geosynchronous altitude. Adv. Space Res. 35, 1313–1317 (2005)
Chao, C.C.: Analytical Investigation of GEO Debris with High Area-to-mass Ratio, AIAA paper No. AIAA-2006-6514. Presented at the 2006 AIAA/AAS Astrodynamics Specialist Conference. Keystone, Colorado (2006)
Cincotta, P. M., Simó, C.,: Simple tools to study global dynamics in non-axisymmetric galactic potentials, Astronomy and Astrophysics. Supplement 147, 205–228 (2000)
Cincotta, P.M., Giordano, C.M., Simó, C.: Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits. Physica D 182, 151–178 (2003)
Delsate, N., Compère, A.: NIMASTEP: a software to modelize, study and analyze the dynamics of various small objects orbiting specific bodies. Astronomy & Astrophysics 540, A120 (2012)
Ferraz-Mello, S.: Analytical study of the Earth’s shadowing effects on satellite orbits. Celestial Mechanics 5, 80–101 (1972)
Hubaux, Ch., Lemaître, A., Delsate, N., Carletti, T.: Symplectic integration of space debris motion considering several Earth’s shadowing models. Adv. Space Res. 49, 1472–1486 (2012)
Hubaux, Ch., Lemaître, A.: The impact of Earth’s shadow on the long-term evolution of space debris. Celest. Mech. & Dyn. Astron. 116, 79–95 (2013)
Hubaux, Ch., Libert, A.-S., Delsate, N., Carletti, T.: Influence of Earth’s shadowing effects on space debris stability. Adv. Space Res. 51, 25–38 (2013)
Laskar, J., Robutel, P.: High order symplectic integrators for perturbed Hamiltonian systems. Celest. Mech. & Dyn. Astron. 80, 39–62 (2001)
Laskar, J.: Frequency analysis of a dynamical system. Celest. Mech. & Dyn. Astron. 56, 191–196 (1993)
Lemaître, A., Delsate, N., Valk, S.: A web of secondary resonances for large A/m geostationary debris. Celest. Mech. & Dyn. Astron. 104, 383–402 (2009)
Rossi, A.: Population models of space debris. In: Knezevic, Z., Milani, A. (eds) Dynamics of population of planetary systems. Proceedings of the IAU Colloquium No. 197, 427–438 (2005)
Rossi, A.: Resonant dynamics of Medium Earth Orbits: space debris issues. Celest. Mech. & Dyn. Astr. 100, 267–286 (2008)
Schildknecht, T., Früh, C., Herzog, A., Hinze, J. & Vananti, A.: AIUB Efforts to Survey, Track, and Characterize Small-Size Objects at High Altitudes. Proceedings of 2010 AMOS Technical Conference, 14-17 September. Maui, Hawaii, USA (2010)
Tommei, G., Milani, A. & Rossi, A.: Orbit determination of space debris: admissible regions. Celest. Mech. & Dyn. Astr. 97, 289–30 (2007)
Valk, S., Lemaître, A., Anselmo, L.: Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios. Adv. Space Res. 41, 1077–1090 (2008)
Valk, S., Lemaître, A., Deleflie, F.: Semi-analytical theory of mean orbital motion for geosynchronous space debris, under gravitational influence. Adv. Space Res. 43, 1070–1082 (2009)
Valk, S., Lemaître, A.: Semi-analytical investigations of high area-to-mass ratio geosynchronous space debris including Earth’s shadowing effects, Adv. Space Res. 42, 1429–1443 (2008)
Valk, S, Delsate, N., Lemaître, A., T.: Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator Adv. Space Res. 43, 1509–1526 (2009)
Yoshida, H.: Construction of higher order symplectic integrators. Phys. Lett. A 150, 262–268 (1990)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lemaitre, A., Hubaux, C. (2014). Space Debris Long Term Dynamics. In: Celletti, A., Locatelli, U., Ruggeri, T., Strickland, E. (eds) Mathematical Models and Methods for Planet Earth. Springer INdAM Series, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-02657-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-02657-2_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02656-5
Online ISBN: 978-3-319-02657-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)