Perturbed Robe’s CR3BP with viscous force

This paper investigates the motion of a test particle (third body) in the frame work of Robe’s circular restricted three-body problem (RCR3BP) when it also experiences the viscous force of the fluid and small perturbations of Coriolis and centrifugal forces. The existence of equilibrium points and their stability are analysed under certain conditions. A pair of axial and an infinite number of circular equilibrium points are observed to exist in the orbital plane of motion, while two equilibrium points, making triangles with the line joining the centre of the spherical shell and the second primary exist in the ‘off-plane’ of motion and thereby are known as ‘out-of-plane’ equilibrium points. The positions of all these equilibrium points are affected by the Viscous force and a small perturbation of the Coriolis force. As regards their stability, both axial points are seen to be asymptotically stable, while the circular and the ‘out-of-plane’ points are unstable. It is noticed that the viscous force improves the results of stability.