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We fit an isothermal oscillatory density model of Uranus' protoplanetary diskto the present-day major satellites and we determine the radial scale length ofthe 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 looklike the Jovian disk that we modeled previously. Its rotation parameter thatmeasures 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 sizeof the disk (only 0.60 Gm). On the other hand, the central density of thecompact Uranian core is higher by a factor of 180 and its core's angularvelocity is about 2.3 times that of Jupiter's core (a rotation period of 3.0 das opposed to 6.8 d). Yet, the rotation of the disk is sufficiently slow toguarantee its long-term stability against self-gravity induced instabilitiesfor millions of years.

Models of a protoplanetary disk forming in-situ the major Uranian satellites before the planet is formed