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Title:
Reorientation of planets with lithospheres: The effect of elastic energy
Authors:
Matsuyama, Isamu; Nimmo, Francis; Mitrovica, Jerry X.
Affiliation:
AA(Carnegie Institution of Washington, Department of Terrestrial Magnetism, 5241 Broad Branch Road NW, Washington, DC 20015, USA), AB(Department of Earth and Planetary Sciences, University of California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA), AC(Department of Physics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 1A7, Canada)
Publication:
Icarus, Volume 191, Issue 2, p. 401-412. (Icarus Homepage)
Publication Date:
11/2007
Origin:
ELSEVIER
DOI:
10.1016/j.icarus.2007.05.006
Bibliographic Code:
2007Icar..191..401M

Abstract

It is commonly assumed that internal energy dissipation will ultimately drive planets to principal axis rotation, i.e., where the rotation vector is aligned with the maximum principle axis, since this situation corresponds to the minimum rotational energy state. This assumption simplifies long-term true polar wander (TPW) studies since the rotation pole can then be found by diagonalizing the appropriate (non-equilibrium) inertia tensor. We show that for planets with elastic lithospheres the minimum energy state does not correspond to principal axis rotation. As the planet undergoes reorientation elastic energy is stored in the deforming lithosphere, and the state of minimum total energy is achieved before principal axis rotation. We find solutions for the TPW of planets that include this effect by calculating the elastic stresses associated with deformation, and then minimizing the total (rotational and elastic) energy. These expressions indicate that the stored elastic energy acts to reduce the effective size of the driving load (relative to predictions which do not include this energy term). Our derivation also yields expressions for the TPW-induced stress field that generalizes several earlier results. As an illustration of the new theory, we consider TPW driven by the development of the Tharsis volcanic province on Mars. Once the size of the Tharsis load and the Mars model is specified, the extended theory yields a more limited range on the possible TPW.
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