  Much theoretical and observational work has been done on stellar winds within
binary systems. We present a new solution for a ballistic wind launched from a
source in a circular orbit. Our method emphasizes the curved streamlines in the
corotating frame, where the flow is steady-state, allowing us to obtain an
exact solution for the mass density at all pre-shock locations. Assuming an
initially isotropic wind, fluid elements launched from the interior hemisphere
of the wind will be the first to cross other streamlines, resulting in a spiral
structure bounded by two shock surfaces. Streamlines from the outer wind
hemisphere later intersect these shocks as well. An analytic solution is
obtained for the geometry of the two shock surfaces. Although the inner and
outer shock surfaces asymptotically trace Archimedean spirals, our tail
solution suggests many crossings where the shocks overlap, beyond which the
analytic solution cannot be continued. Our solution can be readily extended to
an initially anisotropic wind.
