A remarkable periodic solution of the three-body problem in the case of equal masses

Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the ¿Lagrange relative equilibrium¿ in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle