Effect of oblateness and viscous force in the Robe’s circular restricted three-body problem

Abstract

This paper studies the motion of a test particle (third body) in the Robe’s circular restricted three-body problem (CR3BP) when the fluid of the first primary is assumed to be viscous and the shape of the second primary is considered as an oblate spheroid. It is found that the first axial equilibrium point is the centre of the spherical shell, while the second one lies on the line joining the primaries inside the spherical shell. It is also seen that the points on a unit circle centered at the second primary and lying within the spherical shell are equilibrium points, called the circular points. Two more equilibrium points, forming triangles with the primaries, are observed to exist in the ‘off-plane‘ of motion, and they are known as out-of-plane equilibrium points. The positions of all these equilibrium points are not affected by the viscous force, but are, except the centre of the spherical shell, influenced by the oblateness of the second primary. Results of the analysis show that both the axial points are asymptotically stable, while the circular and the out-of-plane points are unstable. It also reveals that the viscous force converts the linear stability into the asymptotic stability.