  Suppose that the initial triangle formed by the three moving masses of the
three-body problem is similar to the triangle formed at some later time. We
derive a simple integral formula for the overall rotation relating the two
triangles. The formula is based on the fact that the space of similarity
classes of triangles forms a two-sphere which we call the shape sphere. The
formula consists of a ``dynamic'' and ``geometric'' term. The geometric term is
the integral of a universal two-form on a``reduced configuration space''. This
space is a two-sphere bundle over the shape sphere. The fibering spheres are
instantaneous versions of the angular momentum sphere appearing in rigid body
motion. Our derivation of the formula is similar in spirit to our earlier
reconstruction formula for the rigid body motion.
