On the Lagrange and Hill Stability of the Motion of Certain Systems with Newtonian Potential

The Lagrange and Hill stability of the motion of point masses moving under the influence of their mutual gravitational attraction are studied. A modified model of the restricted three-body problem is proposed. In accordance with this model, the smallest of the masses is not infinitesimal. This simplifies the study of the Lagrange and Hill stability of the motion. In particular, it is shown that the correctness of the statement of the restricted three-body problem by itself provides the Hill stability of the small-mass point m_3.