On the thickness and evolution of the dust layer during the formation of the solar system

We discuss certain dynamical processes during the final stage of the sinking of the dust layer. We supposed that turbulance gave rise to a state of slow sinking (quasi-equilibrium) and evaluated the critical thickness at the onset of gravitational instability in the radial direction. We gave a precise numerical relation between 3 length-scales: $\text{〈|Z|〉c : h}{}_1\text{: λ}{}_{\mathrm{T}}\text{= 0.02107 : 0.1592 : 1}$, the first being the mean height of the dust particles at the onset of radial instability, the second being that value of the half-thickness and of the height at which the self-gravity of the dust layer is equal to the solar z-component, and the last being the longest wavelength at the onset of ring instability. We also calculated the time required for the formation of rings and found it to be far shorter than the sinking time.