Resonance in the Restricted Problem of Three Bodies with Short-Period Perturbations in the Elliptic Case

  • K. B. Bhatnagar
  • Beena Gupta
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 72)

Abstract

This is a generalization of the paper by Bhatnagar and Beena Gupta ‘Resonance in the restricted problem of three bodies with short-periodic perturbations’. The motion of an asteroid moving in the gravitational field of Jupiter is considered. In the original paper it was assumed that Jupiter is moving in a circular orbit around the Sun. In the present paper we consider the orbit to be elliptic. The series occurring in the problem are expanded in powers of a small parameter ε, which represents the ratio of the mass of Jupiter to that of the Sun. The perturbations in the osculating elements are obtained up to O(ε).

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References

  1. Brouwer, D. and Glemence, G.M.: 1961, Methods of Celestial Mechanics, Academic Press Inc., New York, pp. 582–584.Google Scholar
  2. Giacaglia, G.E.O.: 1969, ‘Resonance in the Restricted Problems of Three Bodies’, Astron. J. 74, No. 10, H–1254–1261.Google Scholar
  3. Bhatnagar, K.B. and Beena Gupta: ‘Resonance in the Restricted Problem of Three Bodies with Short-Periodic Perturbations’, to appear in Porc. Nation. Sci. Acad. India.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • K. B. Bhatnagar
    • 1
  • Beena Gupta
    • 1
  1. 1.Department of MathematicsUniversity of DehliDelhiIndia

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