  We show that any bounded zero-angular momentum solution for the Newtonian
three-body problem must suffer infinitely many eclipses, or collinearities,
provided that it does not suffer a triple collision. Motivation for the result
comes from the dream of building a symbolic dynamics for the three-body
problem, one whose symbols 1, 2, 3 representing the three types of eclipses.
The proof involves the conformal geometry of the shape sphere.
