Some considerations on the homographic solutions of the three body problem

Abstract

This paper deals with the problem of homographic solutions in the case of three bodies. A solution of the problem of tree bodies is homographic (Wintner, "The Analitical Foundations of Celestial Mechanics" page 284) if the configuration of the thee bodies is similar for every time t. The coordinate system of reference needs not to be inertial. Then, we introduce an "heliocentric" coordinate system, with the origin placed in one of the three masses, say m3.