Bifurcation points in the planar problem of three bodies

Abstract

An essential parameter in the planar problem of three bodies is the product of the square of the angular momentum and of the total energy (c ² H). The role of this parameter, which may be called abifurcation parameter, in establishing regions of possible motions has been shown by Marchal and Saari (1975) and Zare (1976a). There exist critical values of this parameter below which exchange between bodies cannot occur. These critical values may be calledbifurcation points.

This paper gives an analytical criterion to obtain these bifurcation points for any given masses of the participating bodies.