L10 From Planetesimals to protoplanets

Orderly growth
Once the gaseous nebula is dispersed (after ~10 Myrs), and all planetesimals have been
accreted into oligarchs, no mechanisms (gas damping, viscous friction) exist any more to
damp the random velocities of the big bodies. Gravitational scattering then increases the
random velocities to v~vesc. This means that the gravitational focussing factor Fg becomes ~1.
The collisional cross section is thus reduced to the geometrical cross section. Growth in this
regime is very slow. Growth of velocity dispersion in the disk is dominated by the
protoplanets, and gravitational focusing is weak.
With Fg =1, the master equation becomes
or in relative terms
This means that the growth rate decreases with increasing mass. Bigger bodies grow slower.
This is the same as in the oligarchic regime. However, Fg is much larger in the oligarchic
regime than in the orderly growth regime.
Orderly growth is the final regime for planet growth, at least in the inner solar system.