Central configurations of the symmetric restricted 4-body problem

We consider the symmetric planar (3+1)- body problem with finite masses m(1) = m(2) = 1, m(3) = mu and one small mass m(4) = epsilon. We count the number of central configurations of the restricted case epsilon = 0, where the finite masses remain in an equilateral triangle configuration, by means of the bifurcation diagram with mu as the parameter. The diagram shows a folding bifurcation at a value consistent with that found numerically by Meyer [9] and it is shown that for small epsilon > 0 the bifurcation diagram persists, thus leading to an exact count of central configurations and a folding bifurcation for small m(4) > 0.