  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, 2015] (tidal dissipation effect depending on the tidal-flexure
frequency) 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
Section 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 axises 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.

General Physics