Relativistic Kepler problem. I. Behavior in the distant past of orbits with gravitational radiation damping

The method of perturbation of orbital elements is used to estimate the effect of the emission of gravitational radiation on the behavior, in the distant past, of the orbit of two weakly gravitationally interacting bodies. The perturbing acceleration due to radiation reaction is computed from time derivatives of the quadrupole moment. All such systems which were bound at finite times were necessarily unbound in the past. This result, while independent of the precise details of the radiation-reaction law, does not follow solely from energy loss due to radiation emission. A consequence of possible astrophysical significance is the possibility of the mutual capture of two bodies from scattering orbits by emission of gravitational radiation