Perturbed Robe’s circular restricted three-body problem under an Oblate Primary

Abstract

This paper examines the existence and linear stability of equilibrium points in the perturbed Robe’s circular restricted three-body problem under the assumption that the hydrostatic equilibrium figure of the first primary is an oblate spheroid. The problem is perturbed in the sense that small perturbations are given to the Coriolis and centrifugal forces are being considered. Results of the analysis found two axial equilibrium points on the line joining the centre of both primaries. It is further observed that under certain conditions, points on the circle within the first primary are also equilibrium points. And a special case where the density of the fluid and that of the infinitesimal mass are equal (D=0) is discussed. The linear stability of this configuration is examined; it is observed that the first axial point is unstable while the second one is conditionally stable and the circular points are unstable.