Self Similar Shocks in Atmospheric Mass Loss Due to Planetary Collisions

Abstract

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 methodologies of Type II self similar solutions. In such solutions, the evolution of the shock wave is determined by boundary conditions at the shock front and a singular point in the shocked region. 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. We demonstrate that, as a planetary shock converges to the self similar solution, it loses information about the collision that created it, including the impact angle for oblique collisions.