The n-body gravitational problem is the mathematical formulation of a question that has fascinated and puzzled astronomers for millennia: How can we predict the motion of the moon and the planets?

According to Isaac Newton's theory of gravitation, any two objects (or "bodies") attract each other by a gravitational force inversely proportional to the square of their distance from each other. Furthermore, Newton's second law of motion states that the acceleration of each body is proportional to the sum of the forces on it from each of the other bodies. Thus, if a certain number (n) of bodies are released at a given time, the acceleration of each one can be computed precisely from the position of the others. Their motion is completely determined, for all time, by their initial positions and velocities.

Newton's theory would appear to be the end of the...