Suppose that you have two bodies interacting only under
the force of gravity (in Newtonian mechanics), and that you are given their
positions, mass, and direction and speed of motion. You can then
calculate rigorously their future movements. However, if we add a
third body, it turns out that there is no general method to calculate
what will happen. Matters get more difficult if we allow many bodies
(so the problem is sometimes called "the n-body problem" or "the many body
problem"). No general solution to this problem exists. This is surprising.
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