  We derive the gravitational radiation-reaction force modifying the Effective
One Body (EOB) description of the conservative dynamics of binary systems. Our
result is applicable to general orbits (elliptic or hyperbolic) and keeps terms
of fractional second post-Newtonian order (but does not include tail effects).
Our derivation of radiation-reaction is based on a new way of requiring energy
and angular momentum balance. We give several applications of our results,
notably the value of the (minimal) "Schott" contribution to the energy, the
radial component of the radiation-reaction force, and the radiative
contribution to the angle of scattering during hyperbolic encounters. We
present also new results about the conservative relativistic dynamics of
hyperbolic motions.
