  The process of gravitational accretion of initially homogeneous gas onto a
solid ball is studied with methods of fluid dynamics. The fluid partial
differential equations for polytropic flow can be solved exactly in an early
stage, but this solution soon becomes discontinuous and gives rise to a shock
wave. Afterwards, there is a crossover between two intermediate asymptotic
self-similar regimes, where the shock wave propagates outwards according to two
similarity laws, initially accelerating, then decelerating (and eventually
vanishing). Lastly, we study the final static state. Our purpose is to attain a
global picture of the process.
