  We present a mathematical model for the propagation of the shock waves that
occur during planetary collisions. Such collisions are thought to occur during
the formation of terrestrial planets, and they have the potential to erode the
planet's atmosphere. We show that under certain assumptions, this evolution of
the shock wave can be determined using the method of self similar solutions.
This self similar solution is of type II, which means that it only applies to a
finite region behind the shock front. This region is bounded by the shock front
and the sonic point. Energy and matter continuously flow through the sonic
point, so that energy in the self similar region is not conserved, as is the
case for type I solutions. Instead, the evolution of the shock wave is
determined by boundary conditions at the shock front and at the sonic point. We
show how the evolution can be determined for different equations of state,
allowing these results to be readily used to calculate the atmospheric mass
loss from planetary cores made of different materials.
