Lunar rotational dissipation in solid body and molten core

Williams, J. G.; Boggs, D. H.; Yoder, C. F.; Ratcliff, J. T.; Dickey, J. O.

doi:10.1029/2000je001396

Cited by 350 publications

(493 citation statements)

References 75 publications

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“…Initial values for ω c used to integrate Eq. (5) as well as values for C c and K are taken from Williams et al (2001) and . These values are kept fixed in our solution and have not been estimated.…”

Section: Analysis Modelmentioning

confidence: 99%

Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Hofmann

Müller

Biskupek

2010

A&A

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Context. Forty years of lunar laser ranging (LLR) data provide an excellent basis to determine various parameters of the Earth-Moon system as well as parameters related to gravitational physics. Aims. We update the Institut für Erdmessung (IfE) LLR model taking the effect of a fluid lunar core into consideration. The temporal variation in the gravitational constantĠ/G 0 and the strong equivalence principle, parameterized by the Nordtvedt parameter η, are investigated. Methods. A set of LLR observations from 1970 to 2009 was analysed and the parameters were determined by a least squares adjustment in two runs. After solving for classical Newtonian parameters (e.g. initial conditions for the lunar orbit and rotation) in the first run, relativistic parameters were determined in the second run. Results. The upper limits to the gravitational constant and the Nordtvedt parameter were found to beĠ/G 0 = (−0.7 ± 3.8)×10 −13 yr −1 and η = (−0.6 ± 5.2) × 10 −4 .

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Section: Analysis Modelmentioning

confidence: 99%

Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Hofmann

Müller

Biskupek

2010

A&A

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“…spin axis orientation and the exact Cassini state location is important, as it can potentially place bounds on energy dissipation due to solid-body tides and core-mantle interactions [Yoder, 1981;Williams et al, 2001]. S. J. Peale et al (Dissipative offset of Mercury's spin axis from Cassini state 1, manuscript in preparation, 2012) examine the magnitude of the offset for various core-mantle coupling mechanisms.…”

Section: Spin Axis Orientationmentioning

confidence: 99%

Mercury's moment of inertia from spin and gravity data

et al. 2012

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[1] Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 AE 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 AE 1.6) arc sec, corresponds to a longitudinal displacement of $450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of Mercury C/MR 2 = 0.346 AE 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is C m /C = 0.431 AE 0.025.

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“…As a consequence of their rapid rotation as well as interaction among the Sun, planets and satellites, many celestial bodies are usually in the shape of a spheroid † Email address for correspondence: kzhang@ex.ac.uk or an ellipsoid and rotating non-uniformly, resulting in libration of those bodies (Dermott 1979;William et al 2001;Noir et al 2009;Baland & Van Hoolst 2010). Planetary libration represents an important dynamic characteristic that has recently been employed to examine the physical properties of planetary interiors (see e.g.…”

Section: Introduction and Formulationmentioning

confidence: 99%

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012

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We consider a homogeneous fluid of viscosity ν confined within an oblate spheroidal cavity, x 2 /a 2 + y 2 /a 2 + z 2 /(a 2 (1 − E 2 )) = 1, with eccentricity 0 < E < 1. The spheroidal container rotates rapidly with an angular velocity Ω 0 , which is fixed in an inertial frame and defines a small Ekman number E = ν/(a 2 |Ω 0 |), and undergoes weak latitudinal libration with frequencyω|Ω 0 | and amplitude Po|Ω 0 |, where Po is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When |ω − 2/(2 − E 2 )| O(E 1/2 ), an asymptotic solution for E 1 and Po 1 in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial-temporal structure of the librating flow. In this case, the librationally driven flow is nonaxisymmetric with amplitude O(Po), and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When |ω − 2/(2 − E 2 )| O(E 1/2 ), the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes O(Po/E 1/2 ) at E 1 and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for E 1 describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at E 1.

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Lunar rotational dissipation in solid body and molten core

Cited by 350 publications

References 75 publications

Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Mercury's moment of inertia from spin and gravity data

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

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