Effects of perturbations in Coriolis and centrifugal forces on the locations and stability of libration points in Robe’s circular restricted three-body problem under oblate-triaxial primaries

Abstract

This paper investigates the effect of small perturbations in Coriolis and centrifugal forces on the axial libration points and their stability in Robe’s circular restricted three-body problem when the hydrostatic equilibrium figure of the first primary is an oblate spheroid; the shape of the second primary is a triaxial rigid body. It is observed that the locations of the axial libration points are only influenced by a small change in the centrifugal force due to the force function Ω being dependent of it. The magnitude of the centrifugal force shift the first libration point (p1,0,0) towards the positive side of the x-axis, while second axial libration (x11+p2,0,0) is shifted away from the origin towards the negative part of the x-axis as a result of the increase in magnitude of the triaxiality and centrifugal force. The range of stability is established and is found that the first axial libration point is stable for p1<0, conditionally stable for 0<p1<c2 and unstable for 0<c2<p1, while the second axial libration point is stable whenever x11<0 and if x11>0, then it is conditionally stable.