Gravitational drag on a point mass in hypersonic motion through a
  gaseous medium
  We explore a ballistic orbit model to infer the gravitational drag force on
an accreting point mass M, such as a black hole, moving at a hypersonic
velocity v_{0} through a gaseous environment of density \rho_{0}. The
streamlines blend in the flow past the body and transfer momentum to it. The
total drag force acting on the body, including the nonlinear contribution of
those streamlines with small impact parameter that bend significantly and pass
through a shock, can be calculated by imposing conservation of momentum. In
this fully analytic approach, the ambiguity in the definition of the lower
cut-off distance $r_{\rm min}$ in calculations of the effect of dynamical
friction is removed. It turns out that $r_{\rm min}=\sqrt{e}GM/2v_{0}^{2}$.
Using spherical surfaces of control of different sizes, we carry out a
successful comparison between the predicted drag force and the one obtained
from a high resolution, axisymmetric, isothermal flow simulation. We
demonstrate that ballistic models are reasonably successful in accounting for
both the accretion rate and the gravitational drag.
