Table of Contents
ISRN Astronomy and Astrophysics
Volume 2013, Article ID 910354, 8 pages
http://dx.doi.org/10.1155/2013/910354
Research Article

Robe's Restricted Three-Body Problem with Variable Masses and Perturbing Forces

1Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria
2Department of Mathematics, College of Science, University of Agriculture, PMB 2373, Makurdi, Nigeria

Received 24 December 2012; Accepted 20 February 2013

Academic Editors: P. P. Avelino, A. Ferrari, P. A. Hughes, and V. Pierrard

Copyright © 2013 Jagadish Singh and Oni Leke. 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

The linear stability of equilibrium points of a test particle of infinitesimal mass in the framework of Robe's circular restricted three-body problem, as in Hallan and Rana, together with effect of variation in masses of the primaries with time according to the combined Meshcherskii law, is investigated. It is seen that, due to a small perturbation in the centrifugal force and an arbitrary constant of a particular integral of the Gylden-Meshcherskii problem, every point on the line joining the centers of the primaries is an equilibrium point provided they lie within the shell. Further, a number of pairs of equilibrium points lying on the -plane and forming triangles with the centers of the shell and the second primary exist, for some values of . The points collinear with the center of the shell are found to be stable under some conditions and the range of stability depends on the small perturbations and , while the triangular points are unstable. Illustrative numerical exploration is given to indicate significant improvement of the problem in Hallan and Rana.