  We present a rigorous calculation of the dynamical friction force exerted on
a spherical massive perturber moving through an infinite homogenous system of
field stars. By calculating the shape and mass of the polarization cloud
induced by the perturber in the background system, which decelerates the motion
of the perturber, we recover Chandrasekhar's drag force law with a modified
Coulomb logarithm. As concrete examples we calculate the drag force exerted on
a Plummer sphere or a sphere with the density distribution of a Hernquist
profile. It is shown that the shape of the perturber affects only the exact
form of the Coulomb logarithm. The latter converges on small scales, because
encounters of the test and field stars with impact parameters less than the
size of the massive perturber become inefficient. We confirm this way earlier
results based on the impulse approximation of small angle scatterings.
