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Nonhydrostatic effects and the determination of icy satellites’ moment of inertia

Gao, Peter and Stevenson, David J. (2013) Nonhydrostatic effects and the determination of icy satellites’ moment of inertia. Icarus, 226 (2). pp. 1185-1191. ISSN 0019-1035. https://resolver.caltech.edu/CaltechAUTHORS:20131121-134151682

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Abstract

We compare the moment of inertia (MOI) of a simple hydrostatic, two layer body as determined by the Radau–Darwin Approximation (RDA) to its exact hydrostatic MOI calculated to first order in the parameter q = Ω^2R^3/GM, where Ω, R, and M are the spin angular velocity, radius, and mass of the body, and G is the gravitational constant. We show that the RDA is in error by less than 1% for many configurations of core sizes and layer densities congruent with those of solid bodies in the Solar System. We then determine the error in the MOI of icy satellites calculated with the RDA due to nonhydrostatic effects by using a simple model in which the core and outer shell have slight degree 2 distortions away from their expected hydrostatic shapes. Since the hydrostatic shape has an associated stress of order ρΩ^2R^2 (where ρ is density) it follows that the importance of nonhydrostatic effects scales with the dimensionless number σ/ρΩ^2R^2, where σ is the nonhydrostatic stress. This highlights the likely importance of this error for slowly rotating bodies (e.g., Titan and Callisto) and small bodies (e.g., Saturn moons other than Titan). We apply this model to Titan, Callisto, and Enceladus and find that the RDA-derived MOI can be 10% greater than the actual MOI for nonhydrostatic stresses as small as ∼0.1 bars at the surface or ∼1 bar at the core–mantle boundary, but the actual nonhydrostatic stresses for a given shape change depends on the specifics of the interior model. When we apply this model to Ganymede we find that the stresses necessary to produce the same MOI errors as on Titan, Callisto, and Enceladus are an order of magnitude greater due to its faster rotation, so Ganymede may be the only instance where RDA is reliable. We argue that if satellites can reorient to the lowest energy state then RDA will always give an overestimate of the true MOI. Observations have shown that small nonhydrostatic gravity anomalies exist on Ganymede and Titan, at least at degree 3 and presumably higher. If these anomalies are indicative of the nonhydrostatic anomalies at degree 2 then these imply only a small correction to the MOI, even for Titan, but it is possible that the physical origin of nonhydrostatic degree 2 effects is different from the higher order terms. We conclude that nonhydrostatic effects could be present to an extent that allows Callisto and Titan to be fully differentiated.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.icarus.2013.07.034DOIArticle
http://www.sciencedirect.com/science/article/pii/S0019103513003357PublisherArticle
https://arxiv.org/abs/1309.1205arXivDiscussion Paper
ORCID:
AuthorORCID
Gao, Peter0000-0002-8518-9601
Stevenson, David J.0000-0001-9432-7159
Additional Information:© 2013 Elsevier Inc. Received 23 April 2013. Revised 18 July 2013. Accepted 31 July 2013. Available online 11 August 2013.
Subject Keywords:Callisto; Enceladus; Ganymede; Interiors
Issue or Number:2
Record Number:CaltechAUTHORS:20131121-134151682
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131121-134151682
Official Citation:Peter Gao, David J. Stevenson, Nonhydrostatic effects and the determination of icy satellites’ moment of inertia, Icarus, Volume 226, Issue 2, November–December 2013, Pages 1185-1191, ISSN 0019-1035, http://dx.doi.org/10.1016/j.icarus.2013.07.034. (http://www.sciencedirect.com/science/article/pii/S0019103513003357)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:42626
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Nov 2013 22:04
Last Modified:09 Mar 2020 13:18

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