Existence and linear stability of triangular points in the perturbed relativistic R3BP when the bigger primary is an oblate spheroid

Abstract

We study the effects of oblateness and small perturbations in the Coriolis and centrifugal forces on the locations and stability of the triangular points in the relativistic R3BP. It is observed that the positions are affected by the oblateness, relativistic, and a small perturbation in the centrifugal force, but are unaffected by that of Coriolis force. It is also seen that the relativistic terms, oblateness, small perturbations in the centrifugal and Coriolis forces influence the critical mass ratio. It is also noticed that all the former three and the latter one possess destabilizing and stabilizing behavior respectively. However, the range of stability increases or decreases according to as p >0 or p<0 where p depends upon the relativistic, oblateness and small perturbations in the Coriolis and centrifugal forces.