  A small mass \mu in orbit about a much more massive black hole M moves along
a world line that deviates from a geodesic of the black hole geometry by
O(\mu/M). This deviation is said to be caused by the gravitational self-force
of the metric perturbation h_{ab} from \mu. For circular orbits about a
non-rotating black hole we numerically calculate the O(\mu/M) effects upon the
orbital frequency and upon the rate of passage of proper time on the worldline.
These two effects are independent of the choice of gauge for h_{ab} and are
observable in principle. For distant orbits, our numerical results agree with a
post-Newtonian analysis including terms of order (v/c)^6.
