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Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

DOI: 10.1155/2013/936859

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Abstract:

The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity. 1. Introduction The present paper is devoted to the analysis of the photogravitational and the oblateness effects of both primaries on the stability of triangular equilibrium points of the planar elliptical restricted three-body problem. The elliptical restricted three-body problem describes the dynamical system more accurately on account that the realistic assumptions of the motion of the primaries are subjected to move along the elliptical orbit. We have attempted to investigate the stability of triangular equilibrium points under the photogravitational and oblateness effects of both the primaries. The bodies of the elliptical restricted three-body problem are generally considered to be spherical in shape, but in actual situations, we have observed that several heavenly bodies are either oblate spheroid or triaxial rigid bodies. The Earth, Jupiter, and Saturn are examples of the oblate spheroid. The lack of sphericity in heavenly bodies causes large perturbation. In addition to the oblateness of heavenly bodies, the triaxiality, the radiation forces of the bodies, the atmospheric drag, and the solar wind are also causes of perturbation. This motivates studies of stability of triangular equilibrium points under the influence of oblateness and radiation of the primaries in the elliptical restricted three-body problem. The stability of the infinitesimal around the triangular equilibrium points in the elliptical restricted three-body problem described in considerable details is due to [1] and the problem was also studied [2–9]. The stability of motion of infinitesimal around one of the triangular equilibrium points ( ) also depends on and . Nonlinear stability of the triangular equilibrium points of the elliptical restricted three-body problem with or without radiation pressure was studied [10–12]. Furthermore, the nonlinear stability of the infinitesimal in the orbits or the size of the stable region around was studied numerically by [11] and the parametric resonance stability around in the elliptical restricted three-body problem has been studied [10]. The

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