  A number of synchronous moons are thought to harbor water oceans beneath
their outer ice shells. A subsurface ocean frictionally decouples the shell
from the interior. This has led to proposals that a weak tidal or atmospheric
torque might cause the shell to rotate differentially with respect to the
synchronously rotating interior. As a result of centrifugal and tidal forces,
the ocean would assume an ellipsoidal shape with its long axis aligned toward
the parent planet. Any displacement of the shell away from its equilibrium
position would induce strains thereby increasing its elastic energy and giving
rise to an elastic restoring torque. We compare the elastic torque with the
tidal torque acting on Europa and the atmospheric torque acting on Titan. For
Europa, the tidal torque is far too weak to produce stresses that could
fracture the ice shell, thus refuting a widely advocated idea. Instead, we
suggest that cracks arise from time-dependent stresses due to non-hydrostatic
gravity anomalies from tidally driven, episodic convection in the interior. Two
years of Cassini RADAR observations of Titan's surface are interpreted as
implying an angular displacement of ~0.24 degrees relative to synchroneity.
Compatibility of the amplitude and phase of the observed non-synchronous
rotation with estimates of the atmospheric torque requires that Titan's shell
be decoupled from its interior. We find that the elastic torque balances the
atmospheric torque at an angular displacement <0.05 degrees, thus coupling the
shell to the interior. Moreover, if Titan's surface were spinning faster than
synchronous, the tidal torque tending to restore synchronous rotation would
certainly be larger than the atmospheric torque. There must either be a problem
with the interpretation of the radar observations, or with our understanding of
Titan's atmosphere and/or interior.
