Advertisement

Astrophysics and Space Science

, Volume 40, Issue 1, pp 201–224 | Cite as

Families of periodic planetary-type orbits in the three-body problem and their stability

  • John D. Hadjidemetriou
Article

Abstract

Several families of the planar general three-body problem for fixed values of the three masses are found, in a rotating frame of reference, where the mass of two of the bodies is small compared to the mass of the third body. These families were obtained by the continuation of a degenerate family of periodic orbits of three bodies where two of the bodies have zero masses and describe circular orbits around a third body with finite mass, in the same direction.

The above families represent planetary systems with the body with the large mass representing the Sun and the two small bodies representing two planets or comets. One section of a family is shown to represent the Jupiter family of comets and also a model for the Sun-Jupiter-Saturn system is found.

The stability analysis revealed that stability exists for small masses and small eccentricities of the two planets. Planetary systems with relatively large masses and eccentricities are proved to be unstable. In particular, the Jupiter family of comets, for small masses of the two small bodies, and the Sun-Jupiter-Saturn system are proved to be stable. Also, it was shown that resonances are not necessarily associated with instabilities.

Keywords

Stability Analysis Periodic Orbit Large Mass Small Body Small Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bozis, G. and Christides, Th.: 1976,Celes. Mech. 12, 277.Google Scholar
  2. Bozis, G. and Hadjidemetriou, J. D.: 1976,Celes. Mech., to appear.Google Scholar
  3. Broucke, R. A. and Boggs, D.: 1975,Celes. Mech. 11, 13.Google Scholar
  4. Broucke, R. A.: 1976,Celes. Mech., to appear.Google Scholar
  5. Delibaltas, P.: 1976, in preparation.Google Scholar
  6. Hadjidemetriou, J. D.: 1975a,Celes. Mech. 12, 155.Google Scholar
  7. Hadjidemetriou, J. D.: 1975b,Celes. Mech.,12, 255.Google Scholar
  8. Hadjidemetriou, J. D. and Christides, Th.: 1975,Celes. Mech. 12, 175.Google Scholar
  9. Hénon, M.: 1974,Celes. Mech. 10, 375.Google Scholar
  10. Moser, J.: 1973,Stable and Random Motions in Dynamical Systems, Princeton Univ. Press.Google Scholar
  11. Standish, E. M.: 1969, in G. E. O. Giagaglia (ed.)Periodic Orbits, Stability and Resonances, D. Reidel Publ. Co., p. 373.Google Scholar
  12. Szebehely, V.: 1967,Theory of Orbits, Academic Press, p. 466.Google Scholar
  13. Szebehely, V.: 1969, in G. E. O. Giagaglia (ed.),Periodic Orbits, Stability and Resonances, D. Reidel Publ. Co., p. 382.Google Scholar

Copyright information

© D. Reidel Publishing Company 1976

Authors and Affiliations

  • John D. Hadjidemetriou
    • 1
  1. 1.University of ThessalonikiThessalonikiGreece

Personalised recommendations