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Celestial Mechanics and Dynamical Astronomy

, Volume 57, Issue 1–2, pp 359–368 | Cite as

Motion of the orbital plane of a satellite due to a secular change of the obliquity of its mother planet

  • Hiroshi Kinoshita
Natural Satellites

Abstract

At the present state the rotational axes of Uranus and Pluto are nearly perpendicular to their orbital planes and each satellite moves in the vicinity of the equatorial plane of its mother planet. We assume that in the past a planet's equatorial plane was nearly coincident with its orbital plane and then the inclination of the equatorial plane with respect to the orbital plane began to increase secularly. Here we discuss whether a satellite that moves in its mother's equatorial plane continues to move in the equatorial plane or not. When the direct solar perturbation is neglected, the satellite continues to stay in the equatorial plane under the condition that the secular rate of change of the obliquity is slower than the precessional speed of the satellite orbital plane with respect to the equator.

Key words

Uranian Satellites Obliquity Change 

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References

  1. Arnold, V.: 1976,Les Méthodes Mathématiques de la Mécanique Classique, NAUKA, Moscou, Chap.6.Google Scholar
  2. Byrd, P.F. and Friedman, M.D.: 1971,Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin.Google Scholar
  3. French, R.G., Elliot, J.L., Levine, S.E.: 1986,Icarus 67, 134.Google Scholar
  4. Goldreich, P.: 1965,Astron.J. 70, 5.Google Scholar
  5. Hori, G.: 1979, in Nomura, T., ed(s).,12 th ISAS Lunar and Planetary Symposium, Institute of Space and Astronautical Science, Tokyo, 166–170.Google Scholar
  6. Kinoshita, H.: 1977,Celest.Mech. 15, 277.Google Scholar
  7. Kinoshita, H.: 1991,Celest. Mech. 52, 293.Google Scholar
  8. Kozai, Y. and Kinoshita, H.: 1973,Celest.Mech. 7, 356.Google Scholar
  9. Landau, L.D. and Lifshitz, E.M.: 1960,Mechanics, Pergamon Press, London, p.133.Google Scholar
  10. Tremaine, S.: 1991,Icarus 89, 85.Google Scholar
  11. Smart, W.M.: 1953,Celestial Mechanics, Longman, London, chap.20.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Hiroshi Kinoshita
    • 1
  1. 1.National Astronomical ObservatoryMitaka, TokyoJapan

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