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We fit an isothermal oscillatory density model of Saturn's protoplanetarydisk to the present-day major satellites and innermost rings D/C and wedetermine the radial scale length of the disk, the equation of state and thecentral density of the primordial gas, and the rotational state of theSaturnian nebula. This disk does not look like the Jovian and Uranian disksthat we modeled previously. Its power-law index is extremely steep ($k=-4.5$)and its radial extent is very narrow ($\Delta R\lesssim 0.9$ Gm), its rotationparameter that measures centrifugal support against self-gravity is somewhatlarger ($\beta_0=0.0431$), as is its radial scale length (395 km); but, as wasexpected, the size of the Saturnian disk, $R_{\rm max}=3.6$ Gm, takes just anintermediate value. On the other hand, the central density of the compactSaturnian core and its angular velocity are both comparable to that ofJupiter's core (density of $\approx 0.3$~g~cm$^{-3}$ in both cases, androtation period of 5.0 d versus 6.8 d); and significantly less than thecorresponding parameters of Uranus' core. As with the other primordial nebulae,this rotation is sufficiently slow to guarantee the disk's long-term stabilityagainst self-gravity induced instabilities for millions of years of evolution.

Models of Saturn's protoplanetary disk forming in-situ its regular satellites and innermost rings before the planet is formed