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The special case of the three body problem, when gravitational potential is given as the Kislik potential

Published online by Cambridge University Press:  05 January 2015

A. Shuvalova  and
T. Salnikova
A. Shuvalova
Affiliation:
Lomonosov Moscow State University, Moscow, 119991, Russia email: a.shuvalova@yahoo.com
T. Salnikova
Affiliation:
Lomonosov Moscow State University, Moscow, 119991, Russia email: tatiana.salnikova@gmail.com
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Abstract

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In this paper we consider the special case of the planar circular restricted three-body problem by the example of the problem of the Earth, the Moon and a point mass, where the gravitational potentials of the Earth and the Moon are given as the Kislik potential. The Kislik potential takes into account the flattening of a celestial body on the poles. We find the relative equilibria solutions for a point mass and analyze their stability. We describe the difference between the obtained points and the classical solution of the three-body problem.

Keywords

celestial mechanicsmethods: analyticalthree-body problemlibration pointflatteninggravitational potential
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 9 , Issue S310: Complex Planetary Systems , July 2014 , pp. 45 - 48
Copyright
Copyright © International Astronomical Union 2014 

References

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Markeev, A. P., 1978, The libration points in celestial mechanics and space dynamics Nauka Moscow.Google Scholar
Worthington, J., 2012, A Study of the Planar Circular Restricted Three Body Problem and the Vanishing Twist Thesis Univ. Sydney.Google Scholar