We fit an isothermal oscillatory density model of Uranus ’ protoplanetary disk to the present-day major satellites and we determine the radial scale length of the disk , the equation of state and the central density of the primordial gas , and the rotational state of the Uranian nebula .
This disk does not at all look like the Jovian disk that we modeled previously .
Its rotation parameter that measures centrifugal support against self-gravity is a lot smaller ( \beta _ { 0 } = 0.00507 ) , as is the radial scale length ( only 27.6 km ) and the size of the disk ( only 0.60 Gm ) .
On the other hand , the central density of the compact Uranian core is higher by a factor of 180 and its core ’ s angular velocity is about 2.3 times that of Jupiter ’ s core ( a rotation period of 3.0 d as opposed to 6.8 d ) .
Yet , the rotation of the disk is sufficiently slow to guarantee its long-term stability against self-gravity induced instabilities for millions of years .