# Characteristics exponents of the triangular solution in the elliptical restricted three body problem under the radiation and oblateness of primaries

## DOI:

https://doi.org/10.14419/ijaa.v3i1.4074## Published:

2015-02-04## Keywords:

Elliptical Restricted Three Body Problem, Stability, Radiation, Oblateness, Binary System.## Abstract

This paper studies effects of the oblateness and radiation of both the primaries on the stability of the infinitesimal motion about triangular equilibrium points (L4,5) in the elliptical restricted three body problem (ER3BP) around the binary system We have exploited analytical method for determining of characteristics exponent to the variational equations with periodic coefficients, developed by Bennet (! 965b), which is based on the Floquet's theory. The stability of the infinitesimal motion about the triangular points under the effects of radiation and oblateness of both the primaries around the binary systems Achird, Luyten726-8, Kruger 60, Alpha Centauri AB and Xi Bootis, has been studied. The stability of infinitesimal around the triangular points has been studied based on the analytical and numerical exploration is simulated by drawing transition curves bounding the region of stability in the (Î¼-e) plane. The region of stability changed with variations in eccentricity, oblateness and radiation pressures. It is observed that the equilibrium points stable in the shaded portion of the transition curve, whereas unstable outside the region of the transition curves.

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