Scalar field self-force effects on orbits about a Schwarzschild black hole

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 (ISCO) 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 $0.122701\times q^2/\mu$, and it increases the angular frequency of the ISCO by the fraction $0.0291657\times q^2/\mu m$.