  We study the tidal interaction between a low-mass companion (e.g., a
protoplanet or a black hole) in orbit about a central mass, and the accretion
disk within which it is submerged. We present results for a companion on a
coplanar orbit with eccentricity e between 0.1 and 0.6. For these
eccentricities, dynamical friction arguments in its local approximation, that
is, ignoring differential rotation and the curvature of the orbit, provide
simple analytical expressions for the rates of energy and angular momentum
exchange between the disk and the companion. We examine the range of validity
of the dynamical friction approach by conducting a series of hydrodynamical
simulations of a perturber with softening radius R_soft embedded in a
two-dimensional disk. We find close agreement between predictions and the
values in simulations provided that R_soft is chosen sufficiently small, below
a threshold value Rtilde_soft, which depends on the disk parameters and on
eccentricity. We give Rtilde_soft for both razor-thin disks and disks with a
finite scaleheight. For point-like perturbers, the local approximation is valid
if the accretion radius is smaller than Rtilde_soft. This condition imposes an
upper value on the mass of the perturber.
