Abstract
This paper deals with the existence and the stability of the libration points in the restricted three-body problem when the smaller primary is an ellipsoid. We have determined the equations of motion of the infinitesimal mass which involves elliptic integrals and then we have investigated the collinear and non collinear libration points and their stability. This is observed that there exist five collinear libration points and the non collinear libration points are lying on the arc of the unit circle whose centre is the bigger primary. Further observed that the libration points either collinear or non-collinear all are unstable.
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