BIFURCATIONS AND ENUMERATION OF CLASSES OF RELATIVE EQUILIBRIA IN THE PLANAR RESTRICTED FOUR-BODY PROBLEM

The planar restricted four-body problem consists of the Newtonian planar three-body problem with an additional body of infinitesimal mass which is attracted by the three bodies (primaries) but has no gravitational effect on them. Relative equilibria are special solutions in which the four bodies rotate uniformly about their center of mass. In a previous article, we proved that the degenerate relative equilibria of the planar restricted four-body problem form a simple, closed, analytic curve. Presently, we complement that work by showing that the bifurcation set in the mass space is a simple, closed, continuous curve, and we use this knowledge to provide the possible numbers of classes of relative equilibria.