Nonlinear Core-Mantle Coupling

Touma, Jihad; Wisdom, Jack

doi:10.1086/321146

Cited by 28 publications

(41 citation statements)

References 34 publications

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“…Following Touma and Wisdom (2001), we describe the core-mantle system, with zero amplitude wobble, by the Hamiltonian…”

Section: Appendixmentioning

confidence: 99%

“…The complete expression for the potential can be found in Touma and Wisdom (2001). Averaging over the orbital period is straightforward and simpler than the analysis in Touma and Wisdom (2001) because we are taking the orbit to be circular. The resulting averaged potential energy is…”

Section: Appendixmentioning

confidence: 99%

“…If the spin axis of the core is slightly displaced from this configuration then the spin axis precesses about the symmetry axis with the core precession frequency ω c (Touma and Wisdom 2001) …”

Section: Introductionmentioning

confidence: 99%

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Precession of the lunar core

Meyer

Wisdom

2011

Icarus

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Abstract:Goldreich (1967) showed that a lunar core of low viscosity would not precess with the mantle.We show that this is also the case for much of lunar history. But when the Moon was close to the Earth the Moon's core was forced to follow closely the precessing mantle, in that the rotation axis of the core remained nearly aligned with the symmetry axis of the mantle. The transition from locked to unlocked core precession occurred between 26.0 and 29.0 Earth radii, thus it is likely that the lunar core did not follow the mantle during the Cassini transition. Dwyer and Stevenson (2005) suggested that the lunar dynamo needs mechanical stirring to power it. The stirring is caused by the lack of locked precession of the lunar core.So, we do not expect a lunar dynamo powered by mechanical stirring when the Moon was closer to the Earth than 26.0 to 29.0 Earth radii. A lunar dynamo powered by mechanical stirring might have been strongest near the Cassini transition.

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“…Following Touma and Wisdom (2001), we describe the core-mantle system, with zero amplitude wobble, by the Hamiltonian…”

Section: Appendixmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Precession of the lunar core

Meyer

Wisdom

2011

Icarus

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“…A quasi-rigid rotational motion of the liquid core has been proposed by many authors (e.g. Sasao et al 1981;Touma & Wisdom 1993), and is often referred to as Poincaré motion (1910), who introduced this notion of "simple motion" in a particularly simple and enlightening way. The Poincaré motion u of the liquid core can be expressed as:…”

Section: Extension: Inertial Couplingmentioning

confidence: 99%

Inertial core-mantle coupling and libration of Mercury

Rambaux

Hoolst²,

Déhant³

et al. 2007

A&A

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The internal structure of Mercury is the most puzzling among the terrestrial planets. The space missions MESSENGER and the upcoming BepiColombo as well as ground-based radar measurements will play an important role in constraining our understanding of the structure, formation, and evolution of Mercury. The development of a complete theory of the coupled spin-orbit motion of Mercury within the Solar System is an essential complement to observational data and will improve significantly our knowledge of the planet. Prior work concerning the effect of core-mantle couplings on the rotation of Mercury has assumed that the obliquity of Mercury is equal to zero and that its orbit is Keplerian. This work deals with the Hermean core-mantle interactions in a realistic model of the orbital and rotational motions of Mercury. To this aim, we have used the SONYR model of the Solar System including Mercury's spin-orbit motion (SONYR is the acronym of Spin-Orbit N-bodY Relativistic model). We studied the dynamical behavior of the rotational motion of Mercury considered as a solid body including either a solid core or a liquid core. The liquid core and the mantle are assumed to be coupled through an inertial torque on the ellipsoidal core-mantle boundary. We determined Mercury's rotation for a large set of interior structure models of Mercury to be able to identify and to clarify the impact of the core motion on the librations. In this paper, we present a comparative study of the librations resulting from different models of the internal structure. The geophysical models have been calculated for a three-layer planet composed of a solid mantle, a liquid outer core, and a solid inner core. We find that (i) the influence of inertial coupling is of the order of a milliarcsecond for a core ellipticity of the order of 10 −4 ; (ii) the amplitude of the 88-day libration depends essentially on the radius of the core or, equivalently, on the concentration of sulfur in the core; and (iii) the range of amplitude values is 19 arcsec, indicating the possibility to discriminate between models of internal structure by using accurate libration measurements.

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“…More recently, Touma and Wisdom (2001) have derived a Hamiltonian formulation on the base of Poincaré's formalism. We will adopt this formalism in what follows.…”

Section: Hamiltonian Formulationmentioning

confidence: 99%

The rotation of Io with a liquid core

Henrard

2008

Celest Mech Dyn Astr

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In a previous paper (Henrard, Celest. Mech. Dyn. Astron. 178, 144-153, 2005c) we have developed an analytical theory of the rotation of the Galilean satellite Io, considered as a rigid body and based on a synthetic theory of its orbital motion due to Lainey (Théorie Dynamique des Satellites Galiléens. PhD dissertation, Observatoire de Paris, 2002) (see also Lainey et al., A&A, 420, 1171Lainey et al., A&A, 420, -1183Lainey et al., A&A, 420, 2004a A&A, 427, 371-376, 2004b). One of the most important causes of departure of the actual rotation from the rigid theory is thought to be the existence of a liquid core, the size of which is unknown but would be an important piece of information concerning the structure of the interior of the satellite. In this contribution we develop the analytical theory of a liquid core contained in a cavity filled by an inviscid fluid of constant uniform density and vorticity. The theory is based on Poincaré (Bull. Astron. 27, 321-356, 1910) model and is developed by a Lie transform perturbation method, very much like in our previous contribution. Our main conclusion is that the addition of a degree of freedom (the spin of the core) with a frequency close to the orbital frequency multiplies the possibility of resonances and that for some particular size of the core one may expect a (possibly small) region of chaotic behaviour in the vicinity of the Cassini state.

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Nonlinear Core-Mantle Coupling

Cited by 28 publications

References 34 publications

Precession of the lunar core

Precession of the lunar core

Inertial core-mantle coupling and libration of Mercury

The rotation of Io with a liquid core

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