In astronomy, the 3-body question is how to calculate exactly the motion of three bodies under the influence of gravity. It is believed that no general solution exists because the situation is chaotic, although Lagrange is famous for coming up with five special cases where the three bodies retain their relative positions.

However I believe I’ve heard somewhere that solutions have been found for a few other special cases besides Lagrange’s original five. Can anyone give me a site/cite for any of these? I tried searching for “three body problem”, but all this gives me are sites devoted to the problem in classical physics of simultaneous elastic collisions between three particles. I need the astronomer’s three-body problem.