Thermal velocity equilibrium in the protoplanetary cloud

In this paper, the temperatures in the planetary nebula are determined based on a competition between cooling by inelastic impacts and heating by gravitational encounters. A kinetic formalism with a Fokker-Planck operator in Landau's form is used to give analytical and simple results. One of the two cases investigated is a one-population disk of planetesimals, which is found to stabilize itself in a quasi-stationary state with a given temperature and a relation for the spread of the orbital elements. The maximum range of the gravitational interaction in this case is determined. In the second case, a disk of planetismals with a distribution of mass, the dynamical friction is found to play a role, and the equilibrium equations for the temperature are easily derived. 20 references