### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 401-412 |

Number of pages | 12 |

Journal | Icarus |

Volume | 191 |

Issue number | 2 |

DOIs | |

State | Published - Nov 15 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Mars
- Planetary formation
- Rotational dynamics

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Icarus*,

*191*(2), 401-412. https://doi.org/10.1016/j.icarus.2007.05.006

**Reorientation of planets with lithospheres : The effect of elastic energy.** / Matsuyama, Isamu M; Nimmo, Francis; Mitrovica, Jerry X.

Research output: Contribution to journal › Article

*Icarus*, vol. 191, no. 2, pp. 401-412. https://doi.org/10.1016/j.icarus.2007.05.006

}

TY - JOUR

T1 - Reorientation of planets with lithospheres

T2 - The effect of elastic energy

AU - Matsuyama, Isamu M

AU - Nimmo, Francis

AU - Mitrovica, Jerry X.

PY - 2007/11/15

Y1 - 2007/11/15

N2 - 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.

AB - 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.

KW - Mars

KW - Planetary formation

KW - Rotational dynamics

UR - http://www.scopus.com/inward/record.url?scp=35448933544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448933544&partnerID=8YFLogxK

U2 - 10.1016/j.icarus.2007.05.006

DO - 10.1016/j.icarus.2007.05.006

M3 - Article

AN - SCOPUS:35448933544

VL - 191

SP - 401

EP - 412

JO - Icarus

JF - Icarus

SN - 0019-1035

IS - 2

ER -