  We describe a special class of ballistic geodesics in Schwarzschild
space-time, extending to the horizon in the infinite past and future of
observer time, which are characterized by the property that they are in 1-1
correspondence, and completely degenerate in energy and angular momentum, with
stable circular orbits. We derive analytic expressions for the source terms in
the Regge-Wheeler and Zerilli-Moncrief equations for a point-particle moving on
such a ballistic orbit, and compute the gravitational waves emitted during the
infall in an Extreme Mass Ratio black-hole binary coalescence. In this way a
geodesic description for the plunge phase of compact binaries is obtained.
