Some consequences of the integral of motion of the center of mass in the three-body problem

Abstract

In this paper, for the general three-body problem, we present some consequences derived from the motion integral of the center of mass. Specifically, if the motion is distal and accompanied by a Hill-stable pair of bodies, then, using the motion integral of the center of mass, we derive the Lagrange stability of the motion in the plane case of the general three-body problem.