  We investigate the gravitational wake due to, and dynamical friction on, a
perturber moving on a circular orbit in a uniform gaseous medium using a
semi-analytic method. This work is a straightforward extension of Ostriker
(1999) who studied the case of a straight-line trajectory. The circular orbit
causes the bending of the wake in the background medium along the orbit,
forming a long trailing tail. The wake distribution is thus asymmetric, giving
rise to the drag forces in both opposite (azimuthal) and lateral (radial)
directions to the motion of the perturber, although the latter does not
contribute to orbital decay much. For subsonic motion, the density wake with a
weak tail is simply a curved version of that in Ostriker and does not exhibit
the front-back symmetry. The resulting drag force in the opposite direction is
remarkably similar to the finite-time, linear-trajectory counterpart. On the
other hand, a supersonic perturber is able to overtake its own wake, possibly
multiple times, and develops a very pronounced tail. The supersonic tail
surrounds the perturber in a trailing spiral fashion, enhancing the perturbed
density at the back as well as far front of the perturber. We provide the
fitting formulae for the drag forces as functions of the Mach number, whose
azimuthal part is surprisingly in good agreement with the Ostriker's formula,
provided Vp t=2 Rp, where Vp and Rp are the velocity and orbital radius of the
perturber, respectively.
