Some Observaties on the Fig8 Solution of the 3BP

Abstract

Some properties of the periodic solution of the three-body problem where three particles of equal mass follow the same trajectory are discussed. This trajectory has the shape of a figure-8. The three particles have a constant separation in time of 1/3 of the period. The angular momentum of the system is zero. The paper by Broucke and Elipe1 gives a thorough overview of history of this solution and places this solution in the general framework of the periodic solutions of the three-body problem. The two most interesting properties are the triangular and collinear configuration. Their occurrence in well known quartic curves with a figure eight shape are collected as an appendix.