  For a particle of mass mu and scalar charge q, we compute the effects of the
scalar field self-force upon circular orbits, upon slightly eccentric orbits
and upon the innermost stable circular orbit of a Schwarzschild black hole of
mass M. For circular orbits the self force is outward and causes the angular
frequency at a given radius to decrease. For slightly eccentric orbits the self
force decreases the rate of the precession of the orbit. The effect of the self
force moves the radius of the innermost stable circular orbit inward by
0.122701 q^2/mu, and it increases the angular frequency of the ISCO by the
fraction 0.0291657 q^2/mu M.
