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Advances in Astronomy
Volume 2014, Article ID 287174, 17 pages
Research Article

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

1Department of Mathematics, Bhilai Institute of Technology, Durg, Chhattisgarh 491001, India
2Department of Mathematics, Rungta College of Engineering & Technology, Bhilai, Chhattisgarh 490024, India

Received 31 January 2014; Revised 28 March 2014; Accepted 1 April 2014; Published 15 May 2014

Academic Editor: Wing Huen Ip

Copyright © 2014 A. Narayan and Amit Shrivastava. 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.


This paper analyzes the existence of resonance stability of the triangular equilibrium points of the planar elliptical restricted three-body problem when both the primaries are oblate spheroid as well as the source of radiation under the particular case, when . We have derived Hamiltonian function describing the motion of infinitesimal mass in the neighborhood of the triangular equilibrium solutions taken as a convergent series. Hamiltonian function for the system has been derived and also expanded in powers of the generalized components of momenta. We have used canonical transformation to make the Hamiltonian function independent of true anomaly. The most interesting and distinguishable results of this study are establishing the relation for determining the range of stability at and near the resonance around the binary system.