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Stability in the Full Two-Body Problem

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Modern Celestial Mechanics: From Theory to Applications

Abstract

Stability conditions are established in the problem of two gravitationally interacting rigid bodies, designated here as the full two-body problem. The stability conditions are derived using basic principles from the N-body problem which can be carried over to the full two-body problem. Sufficient conditions for Hill stability and instability, and for stability against impact are derived. The analysis is applicable to binary small-body systems such as have been found recently for asteroids and Kuiper belt objects.

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References

  • Maciejewski, A. J.: 1995, ‘Reduction, relative equilibria and potential in the two rigid bodies problem’, Celest. Mech. & Dyn. Astr. 63, 1–28.

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  • Scheeres, D. J.: 2001, ‘Changes in rotational angular momentum due to gravitational interactions between two finite bodies’, Celest. Mech. & Dyn. Astr. 81, 39–44.

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI, 48109-2140, USA

    D. J. Scheeres

Authors
  1. D. J. Scheeres
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Italy

    Alessandra Celletti

  2. Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Brazil

    Sylvio Ferraz-Mello

  3. Département de Mathématique, FNDP, Namur, Belgium

    Jacques Henrard

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© 2002 Springer Science+Business Media Dordrecht

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Scheeres, D.J. (2002). Stability in the Full Two-Body Problem. In: Celletti, A., Ferraz-Mello, S., Henrard, J. (eds) Modern Celestial Mechanics: From Theory to Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2304-6_10

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  • DOI: https://doi.org/10.1007/978-94-017-2304-6_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6078-5

  • Online ISBN: 978-94-017-2304-6

  • eBook Packages: Springer Book Archive

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