Bifurcation of Relative Equilibria of the (1+3)-Body Problem

We study the relative equilibria of the limit case of the planar Newtonian 4–body problem when three masses tend to zero, the so-called (1 + 3)–body problem. Depending on the values of the infinitesimal masses the number of relative equilibria varies from ten to fourteen. Always six of these relative equilibria are convex and the others are concave. Each convex relative equilibrium of the (1 + 3)–body problem can be continued to a unique family of relative equilibria of the general 4–body problem when three of the masses are sufficiently small and every convex relative equilibrium for these masses belongs to one of these six families.