On the Lagrange stability of motion in the three-body problem

For the three-body problem, we study the relationship between the Hill stability of a fixed pair of mass points and the Lagrange stability of a system of three mass points. We prove the corresponding theorem establishing sufficient conditions for the Lagrange stability and consider a corollary of the theorem obtained concerning a restricted three-body problem. Relations that connect separately the squared mutual distances between mass points and the squared distances between mass points and the barycenter of the system are established. These relations can be applied to both unrestricted and restricted three-body problems. © 2005 Springer Science+Business Media, Inc.