  An orbiting object in a gas rich environment creates a gravitational density
wake containing information about the object and its orbit. Using linear
perturbation theory, we analyze the observable properties of the gravitational
wake due to the object circularly moving in a static homogeneous gaseous
medium, in order to derive the Bondi accretion radius $r_B$, the orbital
distance $r_p$, and the Mach number of the object. Supersonic motion, producing
a wake of spiral-onion shell structure, exhibits a single-armed Archimedes
spiral and two-centered circular arcs with respect to the line of sight. The
pitch angle, arm width, and spacing of the spiral pattern are entirely
determined by the orbital distance $r_p$ and Mach number of the object. The
arm-interarm density contrast is proportional to the Bondi accretion radius,
decreasing as a function of distance with a power index of -1. The background
density distribution is globally changed from initially uniform to centrally
concentrated. The vertical structure of the wake is manifested as circular arcs
with the center at the object location. The angular extent of the arcs is
determined by the Mach number of the object motion. Diagnostic probes of
nonlinear wakes such as a detached bow shock, an absence of the definite inner
arm boundary, the presence of turbulent low density eddies, and elongated
shapes of arcs are explained in the extension of the linear analysis. The
density enhancement at the center is always $r_B/r_p$ independent of the
nonlinearity, suggesting that massive objects can substantially modify the
background distribution. These detailed understanding of the wake
characteristics will provide an interpretative framework for both further
theoretical works under more complicated situations and future observations to
detect the gravitational wakes of hidden objects.
