"nldmut:  christinetheastrophysicist:  Physicists Discover 13 New Solutions to Three-Body Problem It's the sort of abstract puzzle that keeps a scientist awake at night: Can you predict how three objects will orbit each other in a repeating pattern? In the 300 years since this ""three-body problem"" was first recognized, just three families of solutions have been found. Now, two physicists have discovered 13 new families. It's quite a feat in mathematical physics, and it could conceivably help astrophysicists understand new planetary systems. Read More.  Images/animations:Three-Body Gallery  Excerpts from the paper:Three Classes of Newtonian Three-Body Planar Periodic Orbits  Here we report the results of our ongoing numerical search for periodic collisionless planar solutions with zero-angular-momentum in a two-parameter subspace of (the full four-dimensional space of) scaled zero-angular momentum initial conditions. This subspace is defined as that of collinear configurations with one body exactly in the middle between the other two, with vanishing angular momentum and vanishing time derivative of the hyper- radius at the initial time. … … Montgomery [21] noticed the connection between the ""fundamental group of a two sphere with three punctures,"" i.e., the ""free group on two letters"" ( a,b ), and the conjugacy classes of the ""projective coloured or pure braid group"" of three strands PB 3 . Graphically, this method amounts to classifying closed curves according to their topologies on a sphere with three punctures. A stereographic projection of this sphere onto a plane, using one of the punctures as the ""north pole"" effectively removes that puncture to infinity, and reduces the problem to one of classifying closed curves in a plane with two punctures. That leads to the aforementioned free group on two letters ( a,b ), where (for definiteness) a denotes a clockwise full turn around the right-hand-side puncture, and b denotes the counterclockwise full turn around the other puncture"
{}