  Compressible flows around blunt objects have diverse applications, but
current analytic treatments are inaccurate and limited to narrow parameter
regimes. We show that the gas-dynamic flow in front of an axisymmetric blunt
body is accurately derived analytically using a low order expansion of the
perpendicular gradients in terms of the parallel velocity. This reproduces both
subsonic and supersonic flows measured and simulated for a sphere, including
the transonic regime and the bow shock properties. Some astrophysical
implications are outlined, in particular for planets in the solar wind and for
clumps and bubbles in the intergalactic medium. The bow shock standoff distance
normalized by the obstacle curvature is $\sim 2/(3g)$ in the strong shock
limit, where $g$ is the compression ratio. For a subsonic Mach number $M$
approaching unity, the thickness $\delta$ of an initially weak, draped magnetic
layer is a few times larger than in the incompressible limit, with
amplification $\sim ({1+1.3M^{2.6}})/({3\delta})$.
