EXISTENCE AND LINEAR STABILITY OF EQUILIBRIUM POINTS IN ROBE'S RESTRICTED THREE BODY PROBLEM WHEN THE PRIMARIES ARE OBLATE SPHEROIDS

摘要

The existence and linear stability of equilibrium points in the Robe's restricted three body problem have been studied after considering the full buoyancy force as in Plastino and Plastino and by assuming the hydrostatic equilibrium figure of the first primary as an oblate spheroid and the second primary also as an oblate spheroid. The pertinent equations of motion are derived and existence of all equilibrium points is discussed. It is found that there is an equilibrium point near the center of the first primary. Further there can be one more equilibrium point on the line joining the centers of the primaries and infinite number of equilibrium points lying on a circle in the orbital plane of the second primary provided the parameters occurring in the problem satisfy certain conditions. So, there can be infinite number of equilibrium points contrary to the classical restricted three body problem. The circular points are unstable and the equilibrium points lying on the line joining the centers of the primaries are stable or unstable depending upon the parameters of the problem satisfying certain conditions.