They approximated disk particles as particles in a box and tracked the evolution of the mass distribution function at individual regions of the disk, modeling velocity evolution, accretion, and rebounding of the disk particles. They showed that, in general, many small moonlets are formed initially rather than a single large moon and concluded that the simplest way to form the present-sized moon is to begin with at least a lunar mass of material outside the Roche limit. However, in gas dynamic calculations it is difficult to include non-local effects such as radial migration of the disk material and global interaction between formed moons and the disk. The importance of the radial diffusion out from the Roche limit has been pointed out through analytical argument9. The sequence of accretion of the moon from an impactgenerated disk may be as follows.
Solid particles condense due to cooling of the disk, possibly after some radial migration.
Subsequent collisions and fragmentation of the particles would damp initially large orbital eccentricities and inclinations of the particles to moderate values in a few orbital periods. We do not pursue such long time evolution here. We present the results of 27 simulations with different initial disk conditions. We also found that the final moon mass is mostly determined by a simple function of initial total mass and angular momentum of the disk. In order to estimate the final moon mass, we do not need to know the details of initial mass, size, and velocity distributions of the disk particles.