Existence and stability of equilibrium points in the perturbed R3BP with Stokes drag in the binary $$\eta -$$ Cassiopeiae system

This paper investigates the motion of an exoplanet in the gravitational field of the binary $$\eta -$$ Cassiopeiae system under the effect of Coriolis, centrifugal and Stokes drag (SD) forces of the binary system. We consider the plane motion of the primaries in the case where $$\eta -$$ Cassiopeiae A and B are triaxial and oblate spheroidal bodies, respectively. In particular, we examine the existence, position, and nature of motion around the equilibrium points under the influence of the system parameters. It is found that under constant SD effect, collinear equilibrium points cease to exist numerically, but there are in the absence of the perturbing force. By a numerical investigation, it is found that there may be three, five, seven, nine or eleven non-collinear equilibria, depending on the values of the system parameters. Additionally, the positions of these points depend on all the system parameters except small perturbation in the Coriolis force. The mathematical model of this problem has been examined for the location and stability of the five non-collinear equilibrium points. A numerical exploration is performed using the binary $$\eta -$$ Cassiopeiae system to compute the position of the equilibrium points and their stability. The positions of these equilibrium points are affected by the presence of perturbations, since they are deviated from their classical positions. The linear stability of the equilibrium points under the combined influence of the mass ratio and the perturbing forces is analyzed, and it is found that all the equilibrium points are unstable except $$L_{4}$$ and $$L_{5}$$ , which are stable for certain parameter values.