Stability of Libration Points Around L_(4,5) with Oblateness Primaries and Circumbinary Disc in Elliptic Restricted Three-Body Problem

Abstract

The present paper considers the restricted three-body problem (R3BP) in  elliptic framework when both primaries are  oblate spheroids and enclosed by a circumbinary disc. The investigation has been carried out both analytically and numerically, the effects of oblateness of the primaries together with the gravitational potential from a disc on the triangular equilibrium L_4,5 and their linear stability of the system, The effect of the oblateness of the more massive primary, circumbinary  disc and eccentricity on the location of triangular points show a move towards the line joining the primaries while increase in oblateness of less massive primary causes a  significant shift towards the origin on  - axis. All the  perturbations reduces the range of stability  of the triangular points, except gravitational potential from the disc which increases the stability region, Where  is the critical mass parameter depends on the parameters involved, which shows that circumbinary disc has stabilizing tendency.