<P> In classical mechanics, the two - body problem is to determine the motion of two point particles that interact only with each other . Common examples include a satellite orbiting a planet, a planet orbiting a star, two stars orbiting each other (a binary star), and a classical electron orbiting an atomic nucleus (although to solve the electron / nucleus 2 - body system correctly a quantum mechanical approach must be used). </P> <P> The two - body problem can be re-formulated as two one - body problems, a trivial one and one that involves solving for the motion of one particle in an external potential . Since many one - body problems can be solved exactly, the corresponding two - body problem can also be solved . By contrast, the three - body problem (and, more generally, the n - body problem for n ≥ 3) cannot be solved in terms of first integrals, except in special cases . </P>

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