The rocket effect on a gravitating mass-losing object

Axisymmetric hydrodynamic calculations on an interaction between a gravitating object and ambient gas are performed. We have computed subsonic and supersonic flows past a mass-losing object in inviscid gas, and the drag coefficient is estimated. The drag coefficient C_d normalized by the accretion radius is found to obey the formula $$C_\text d =2\enspace\text{log}(r_\text{max}/r_\text{min})+C$$, where $$r_\text{max}$$ and $$r_\text{min}$$ are the cut-off distances of gravity and C is constant, if the object is moving supersonically in the gas. If the velocity of the ejected wind is supersonic, the constant C is negative and we have a thrust rather than a drag supposing $$r_\text{max}$$ not to be too large. If the object is moving subsonically, there is no logarithmic term and we have a genuine thrust, which may be called the rocket effect.