Existence and Stability of the Libration Points in the Circular Restricted Three Body Problem with Variable Masses

We have investigated the existence and stability of the libration points in the circular restricted three body problem with the variation of all the masses (primaries and infinitesimal body) with time. We have used the Meshcherskii transformation for finding the autonomized equations of motion and found at most nine libration points. We have drawn the zero velocity curves and Poincare surface of sections for the different values of parameter k. Finally, we have checked the stability and found that all the libration points are unstable.