Three Body Problem (celestial mechanics)

The Three Body Problem is a physics and mathematics problem arising in the field of celestial mechanics and astronomy. The question is to predict the spacetime trajectories of three (point) masses under the influence of Newtonian gravity (inverse square law). This problem is currently unsolved for all but simple cases. No closed form solution is known in general, but progress has been made using computer simulations. The intractable part arises from the unpredictability of the chaotic dynamics induced by three bodies.

Taking into account general relativity makes the problem significantly harder.

By contrast, the two body problem of classical physics is completely solved.

Newtonian gravity
Newton postulated that the gravitational interaction between two objects follows an inverse square law


 * $$F_{12} = Gm_1m_2 / r_{12}^2$$

where $$m_1, m_2$$ are the point masses and $$r_{12}$$ is the distance between them. $$G$$ is called the 'universal gravitation constant'.