Effect of Perturbations in the Coriolis and Centrifugal Forces on the Location and Stability of the Equilibrium Solutions in Robe’s Restricted Problem of 2+2 Bodies

In this problem, one of the primaries of mass m1 is a Roche Ellipsoid filled with a homogeneous incompressible fluid of density ρ1. The smaller primary of mass m2 is a point mass outside the Ellipsoid. The third and the fourth bodies (of mass m3 and m4 respectively) are small solid spheres of density ρ3 and ρ4 respectively inside the Ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m2 is describing a circle around m1. The masses m3 and m4 mutually attract each other, do not influence the motions of m1 and m2 but are influenced by them. In this paper, we have studied the effect of perturbations in the coriolis and centrifugal forces on the location and stability of the equilibrium points in Robe’s restricted problem of 2+2 bodies with the bigger primary a Roche ellipsoid (Chandrashekhar,1987). We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii)that originating in the attraction of m2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m3 and m4 and their linear stability are analyzed. We have proved that there exist only six equilibrium solutions of the system, provided they lie within the Roche Ellipsoid. In a system where the primaries are considered as earth-moon and m3,m4 as icebergs, the equilibrium solutions of m3 and m4 respectively when the displacement is given in the direction of x1− axis or x2− axis are unstable. Robe’s Restricted Problem; Roche Ellipsoid; Equilibrium Solution; Stability; Buoyancy Force.