Existence and differential geometric properties of continuous families of periodic three-body motions with non-uniform mass distributions

Using the method of analytic continuation in an equivariant differential geometric setting, we exhibit two interesting families of vanishing angular momentum periodic orbits for the Newtonian three-body problem with non-uniform mass distributions having two equal masses which connect at the celebrated figure-8 orbit, exhibited by A. Chenciner and R. Montgomery (2000) in the case of equal masses, and yield a continuous family of periodic three-body motions in the plane.At one end of the family, when the two equal masses are infinitesimal and the third one reaches the value of +1, we arrive at a solution of a double Kepler problem; at the other end of the family, when the third mass is infinitesimal, we have a special case of periodic solution of a restricted three-body problem.