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 = µ and one small mass m ₄ = . We count the number of central configurations of the restricted case = 0, where the finite masses remain in an equilateral triangle configuration, by means of the bifurcation diagram with 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 > 0 the bifurcation diagram persists, thus leading to an exact count of central configurations and a folding bifurcation for small m ₄ > 0.