On the formation of the planetary system the titius-bode law

The linear density and velocity perturbations are analyzed in a differentially rotating thin gravitating disc consisting of gas and dust. For the radial behaviour of the equilibrium density and the velocity of sound we assume a power law. The zeros of these perturbations have a distance behaviour like the distances of the planets and their satellites known as the Titius-Bode rule. It is suggested, that the knots of the velocity disturbances are the places where ring like dust accumulations occur. The mechanism is the same as in the Kundt's tube, where collisions between the dust and the oscillating gas are responsible for this effect.