Effect of perturbations in coriolis and centrifugal forces on the location and stability of the equilibrium point in the Robeʹs circular restricted three body problem

The location and stability of the equilibrium point in the Robeʹs (Celest. Mech. 16 (1977) 343) circular restricted three body problem with the density ρ1 of the fluid filling one of the primaries, a rigid spherical shell and ρ3, the density of the infinitesimal body being equal, have been studied when small perturbations ε and ε′ are given to the coriolis and centrifugal forces, respectively. It is proved that there is only one equilibrium point which lies on the right or left of the center of the shell on the line joining the center of the shell and the second primary accordingly as ε′ is positive or negative and the change ε in the coriolis force does not affect the location of the equilibrium point. Further, it is seen that the range of stability increases or decreases depending upon whether the point (ε,ε′) lies in one or the other of the two regions in which the (ε,ε′) plane is divided by the line 4325 ε′−103ε=0.