Calculation of Infall Heating at the Surfaces of Model Solar Nebulae

This work attempts to estimate the temperature rise of infalling interstellar gas and dust as it accreted to the surfaces of the primitive solar nebula, where its velocity was checked and its kinetic energy was dissipated as heat. First a simple ballistic collapse model is set up. Input parameters are the mass of interstellar material undergoing collapse, its mean specific angular momentum, and the stage of collapse under consideration. Second, the state parameters are determined for gas arriving at various radial distances on the nebular surfaces during this particular stage of collapse. The infalling gas arrives at supersonic velocities, and encounters a standing shock front at the nebular surfaces. The change in state parameters (including the temperature rise) of the gas when it crosses the shock front is calculated. Third, the temperature rise of infalling solid particles is calculated. These are not stopped at the shock front, but are decelerated by aerodynamic drag in the body of the nebula, much like meteors in the terrestrial atmosphere. Finally, summations are made of the distribution of mass from all stages of infall in several nebula models with different initial parameters. These are compared with the present distribution of planetary mass in the solar system.