  An extended gravitational object embedded in a parent system comprised of gas
and collisionless particles may undergo both dynamical friction (DF) and mass
loss by tidal forces. If the object is compact enough, it can increase its mass
through accretion of material from the surrounding medium. We extend the
classical linear analysis of DF on a constant-mass body in a gaseous medium to
the case where its mass changes with time. We show that the structure of the
wake may differ significantly from the constant-mass case. For instance, the
front-back symmetry of density about subsonic constant-mass perturbers is
broken down for variable-mass perturbers. The density wake keeps a memory of
the past mass history of the perturber. For dissolving perturbers, the density
field is more dense than expected using the instantaneous mass of the perturber
in the classical formula. As a consequence, the instantaneous-mass
approximation underestimates the drag force for mass-losing perturbers and
overestimates it for mass-gaining perturbers. We present cases in which the
percentage error in the drag force using the instantaneous-mass approximation
is greater than 50%.
