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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 679063, 18 pages
http://dx.doi.org/10.1155/2012/679063
Research Article

Existence and Linear Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Oblateness

1Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria
2Department of Mathematics Statistics and Computer Science, College of Science and Technology, Kaduna Polytechnic, Kaduna, Nigeria

Received 26 March 2012; Accepted 2 July 2012

Academic Editor: Burak Polat

Copyright © 2012 Jagadish Singh and Abubakar Umar Sandah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.