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

Published online by Cambridge University Press:  12 April 2016

K. B. Bhatnagar  and
Beena Gupta
K. B. Bhatnagar
Affiliation:
Department of Mathematics, University of Dehli, Delhi, India
Beena Gupta
Affiliation:
Department of Mathematics, University of Dehli, Delhi, India

Abstract

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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 0(ε).

Type
Part V. Gravitational Problem of three or more bodies
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 339 - 353
Copyright
Copyright © Reidel 1978

References

Brouwer, D. and Glemence, G.M.: 1961, Methods of Celestial Mechanics, Academic Press Inc., New York, pp. 582–84.Google Scholar
Giacaglia, G.E.O.: 1969, ‘Resonance in the Restricted Problems of Three Bodies’, Astron. J. 74, No. 10, H-1254–61.CrossRefGoogle Scholar
Bhatnagar, K.B. and Beena, Gupta: ‘Resonance in the Restricted Problem of Three Bodies with Short-Periodic Perturbations’, to appear in Porc. Nation. Sai. Acad. India.Google Scholar