Some special restricted four-body problems—II. From Caledonia to Copenhagen

Special analytical solutions are determined for restricted, coplanar, four-body equal mass problems, including the Caledonian problem, where the masses Mi = M for i = 1,2,3,4. Most of these solutions are shown to reduce to the Lagrange solutions of the Copenhagen problem of three bodies by reducing two of the masses (mi = m for i = 1,2) in the four-body equal mass problem to zero while maintaining their equality of mass. In so doing, families of special solutions to the four-body problem are shown to exist for any value of the mass ratio μ = mM.