About influence of differential rotation in convection zone of gaseous or fluid giant planet (Uranus) onto the parameters of orbits of satellites

Tidal interactions between planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. We suggest in the current research to take into consideration the additional well-known effect of differential rotation which obviously takes place in the gaseous or fluid convection zone of primary giant planet (indeed, the aforementioned effect exists even not depending on the orbital evolution of satellites around host planet). Nevertheless, estimations for the contribution of the aforementioned effect of differential rotation in the Uranus system (including all its most massive satellites) let us exclude using such effect from calculations of mutual evolution of the eccentricity e along with the semi-major axis a for all satellites of Uranus (planet of ice type). It means that the Uranus can be considered in the analytic exploration of governing equations as to be the appropriate candidate for applying the modern ansatz (Efroimsky in Astron J 150:98, 2015) (tidal dissipation effect depending on the tidal-flexure frequency chi) in regard to estimations of eccentricity e along with semi-major axis a for satellites of Uranus. We can see from the results of calculations in Sect. 3 that the combined system of governing equations (in the sense of combined contributions to the tidal dissipation from Uranus + from satellite) yields the really observed magnitudes of decelerations for semi-major axes of all the satellites of Uranus. Meanwhile, internal heat generation effects in the satellites (due to tidal dissipation effect) are much more than those which definitely take place in the Uranus, excepting the case of Ariel.

Automated summary

The study examines the effects of tidal interactions and differential rotation on the orbital evolution of Uranus satellites, finding that the differential rotation effect has minimal contribution in the Uranus system. Uranus is considered suitable for applying modern ansatz to analyze the characteristics of satellite orbits, with internal heat generation effects primarily occurring within the satellites.