Existence and Linear Stability of Equilibrium Points in the Robe's Restricted Three-Body Problem with Oblateness. (15th August 2012)

• Record Type: Journal Article
• Authors: Singh, Jagadish; Umar Sandah, Abubakar
• Other Names: Polat Burak Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2012(2012)
• Publication Date: 2012-08-15
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2012/679063
• Languages: English
• ISSNs: 1687-9120

Abstract

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.