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Elastic ice shells of synchronous moons: Implications for cracks on Europa and non-synchronous rotation of Titan

Goldreich, Peter M. and Mitchell, Jonathan L. (2010) Elastic ice shells of synchronous moons: Implications for cracks on Europa and non-synchronous rotation of Titan. Icarus, 209 (2). pp. 631-638. ISSN 0019-1035.

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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. Applications along these lines have been made to Europa and Titan. However, the shell is coupled to the ocean by an elastic torque. 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. In the investigation reported on here, the elastic torque is compared with the tidal torque acting on Europa and the atmospheric torque acting on Titan. Regarding Europa, it is shown that the tidal torque is far too weak to produce stresses that could fracture the ice shell, thus refuting an idea that has been widely advocated. Instead, it is suggested that the cracks arise from time-dependent stresses due to non-hydrostatic gravity anomalies from tidally driven, episodic convection in the satellite’s interior. Two years of Cassini RADAR observations of Titan’s surface have been interpreted as implying an angular displacement of ~0.24° relative to synchronous rotation. 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 seasonal atmospheric torque at an angular displacement ≾0.05°, effectively 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 almost certainly be larger than the atmospheric torque. There must either be a problem with the interpretation of the radar observations, or with our basic understanding of Titan’s atmosphere and/or interior.

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Additional Information:© 2010 Elsevier. Received 30 September 2009; revised 16 April 2010; accepted 16 April 2010. Available online 24 April 2010. We thank Jay Melosh and an anonymous referee for helpful comments, Zane Selvans for informative conversations and David Stevenson for wise counsel. J.L.M. was supported by the W.M. Keck Foundation at the Institute for Advanced Study.
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W. M. Keck Foundation at the Institute for Advanced StudyUNSPECIFIED
Subject Keywords:Europa; Titan; Resonances, Spin–orbit
Issue or Number:2
Record Number:CaltechAUTHORS:20101025-133610473
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20512
Deposited By: Tony Diaz
Deposited On:13 Nov 2010 03:42
Last Modified:03 Oct 2019 02:11

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