The problem of computing the mutual gravitational interaction of three masses. This problem is surprisingly difficult to solve, even in the so called restricted three-body problem, corresponding to the simple case of the three masses moving in a common plane.
Bruns' Theorem, Lagrange Points, Many-Body Problem, n-Body Problem, Planar Orbit, Poincaré's Theorem, Restricted Three-Body Problem, Two-Body Problem
References
Barrow-Green, J. Poincaré and the Three Body Problem. Amer. Math. Soc., 1996.
Basdevant, J.-L. and Dalibard, J. "Exact Results for the Three-Body Problem." Ch. 5 in The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics. Berlin: Springer-Verlag, pp. 61-68, 2000.
Whittaker, E. T. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies. New York: Dover, 1944.
