  A particle of mass $\mu$ moves on a circular orbit of a nonrotating black
hole of mass $M$. Under the restrictions $\mu/M \ll 1$ and $v \ll 1$, where $v$
is the orbital velocity, we consider the gravitational waves emitted by such a
binary system. We calculate $\dot{E}$, the rate at which the gravitational
waves remove energy from the system. The total energy loss is given by $\dot{E}
= \dot{E}^\infty + \dot{E}^H$, where $\dot{E}^\infty$ denotes that part of the
gravitational-wave energy which is carried off to infinity, while $\dot{E}^H$
denotes the part which is absorbed by the black hole. We show that the
black-hole absorption is a small effect: $\dot{E}^H/\dot{E} \simeq v^8$. We
also compare the wave generation formalism which derives from perturbation
theory to the post-Newtonian formalism of Blanchet and Damour. Among other
things we consider the corrections to the asymptotic gravitational-wave field
which are due to wave-propagation (tail) effects.
