A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth

Sasao, Tetsuo; Okubo, Shuhei; Saitô, Masanori

doi:10.1007/978-94-010-9568-6_27

Cited by 160 publications

(134 citation statements)

References 15 publications

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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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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 second group of theories builds the equations of t, he system by means of classical mechanics [e.g., Molodensky, 1961; Sasao et al, 1980;Mathews et al, 1991aMathews et al, , 1991b. In this way the general equations of the angular momentum conservations are stated for the whole Earth and its layers.…”

mentioning

confidence: 99%

Canonical approach to the free nutations of a three‐layer Earth model

Escapa¹,

Getino²,

Ferrándiz³

2001

J. Geophys. Res.

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“…The angular momentum balance equations for the whole Earth and the liquid core relate the angular velocity vectors of the whole Earth, ω, and of the liquid core, ω f , to the potential. In an Earth-fixed frame of reference, the equations for the equatorial component ω = ω 1 + iω 2 are (see, e.g., Sasao et al 1980;Hinderer et al 1987):…”

Section: The Earth's Variable Rotationmentioning

confidence: 99%

“…The relations between our notations and the notation used in Sasao et al (1980) or Mathews et al (2002) is provided in Table 1. Notice that in the literature, one usually writes ω = Ωm = Ω(m 1 + im 2 ) and considers the above equations for m only.…”

Section: The Earth's Variable Rotationmentioning

confidence: 99%

Impact of tidal Poisson terms on nonrigid Earth rotation

Folgueira

Déhant²,

Lambert³

et al. 2007

A&A

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Context. The tidal potential generated by bodies in the solar system contains Poisson terms, i.e., periodic terms with linearly timedependent amplitudes. The influence of these terms on the Earth's rotation, although expected to be small, is of interest for high accuracy modeling. Aims. Therefore, we study their contribution to the rotation of a non-rigid Earth with an elastic mantle and liquid core. Methods. Starting from Liouville's equations, and following an analytical treatment, we obtain the relations accounting for Poisson terms in the forcing and providing the solution for the wobble. Results. We show that the transfer function between rigid and non rigid nutation amplitudes, as usually defined in the literature, must be supplemented by additional terms proportional to the amplitude of the Poisson term of the potential. These new terms are inversely proportional to (σ − σ N ) 2 where σ is the forcing frequency and σ N are the eigenfrequencies associated with the retrograde free core nutation and the Chandler wobble. The highest contribution to the nutation is 6 µas (∆ψ) on the term 2l − 2F + 2D − 2Ω and remains below 1 µas for the other terms. A contribution of 88 µas/cy is found to the obliquity rate. We evaluate the variations of the third component of the wobble of the Earth and of the core in response to a zonal tidal potential, and show that there is no significant change.

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A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth

Cited by 160 publications

References 15 publications

Inertial core-mantle coupling and libration of Mercury

Inertial core-mantle coupling and libration of Mercury

Canonical approach to the free nutations of a three‐layer Earth model

Impact of tidal Poisson terms on nonrigid Earth rotation

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