Studying stability of the equilibrium solutions in the restricted Newton's problem of four bodies

Newton's restricted problem of four bodies is investigated. It has been shown that there are six equilibrium solutions of the equations of motion. Stability of these solutions is analyzed in linear approximation with computer algebra system Mathematica. It has been proved that four radial solutions are unstable while two bisector solutions are stable if the mass of the central body $P_0$ is large enough. There is also a domain of instability of the bisector solutions near the resonant point in the space of parameters and its boundaries are found in linear approximation.