  We present results of numerical calculations showing a three-body orbit's
period's $T$ dependence on its topology. This dependence is a simple linear
one, when expressed in terms of appropriate variables, suggesting an exact
mathematical law. This is the first known relation between topological and
kinematical properties of three-body systems. We have used these results to
predict the periods of several sets of as yet undiscovered orbits, but the
relation also indicates that the number of periodic three-body orbits with
periods shorter than any finite number is countable.
