Effects of a physical librations of the moon caused by a liquid core, and determination of the fourth mode of a free libration

Barkin, Yu. V.; Hanada, Hideo; Matsumoto, Koji; Sasaki, Sho; Barkin, M. Yu.

doi:10.1134/s003809461406001x

Cited by 12 publications

(3 citation statements)

References 8 publications

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“…Also, as we have already noted, having N fcn 1, considerably reduces the amplitude of the resonance. Indirect observation of the FCN based on its resonance with weaker modes of physical libration have been proposed (Barkin et al 2014;Petrova et al 2018). Our results show that such measurements would not give T fcn directly, but rather a value 10% smaller.…”

Section: Implications For Mars and The Moonmentioning

confidence: 54%

Free Core Nutation and its relation to the Spin-Over Mode

Rekier¹

2022

Preprint

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The time-varying response of the Earth's and other planets' rotation to external gravitational torques depends strongly on their internal structure. In particular, the existence of the mode known as the Free Core Nutation in the fluid core, is known to amplify the forced nutations in the near-diurnal retrograde frequency band (as measured in the planetary frame of reference). Due to their proximity in shape and frequency, this mode is sometimes equated with the so-called Spin-Over Mode which denotes the free oscillation of a steadily rotating ellipsoidal fluid core. Through a careful study of the freely rotating two-layer planetary model with a rigid mantle and an inviscid fluid core, we show that the Spin-Over Mode frequency corresponds to that where the sum of the external and internal torques on the mantle are balanced, causing it to rotate steadily. The presence of dissipation at the Core-Mantle Boundary causes the Free Core Nutation to become damped and slightly offset its resonance frequency. We show that this offset, which is ≈ −1 day for the Earth, can be interpreted as the result of the proximity of the Free Core Nutation frequency to that of the Spin-Over Mode, which now corresponds to a minimum in the magnitude of the transfer function for nutations. We also show how this proximity leads to a slightly lower Quality factor for the resonance than that compute from the usual formula. We conclude by discussing possible implications of this mechanism for Mars, the Moon, and the long-term evolution of the Earth.

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Section: Implications For Mars and The Moonmentioning

confidence: 54%

Free Core Nutation and its relation to the Spin-Over Mode

Rekier¹

2022

Preprint

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“…In addition, as we have already noted, having N 1 fcn  considerably reduces the amplitude of the resonance. Indirect observation of the FCN based on its resonance with weaker modes of physical libration has been proposed (Barkin et al 2014;Petrova et al 2018). Our results show that such measurements would not give T fcn ☾ directly, but rather a value 10% smaller.…”

Section: Implications For Mars and The Moonmentioning

confidence: 54%

Free Core Nutation and Its Relation to the Spin-over Mode

Rekier

2022

Planet. Sci. J.

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The time-varying response of Earth’s and other planets’ rotation to external gravitational torques depends strongly on their internal structure. In particular, the existence of the mode known as the free core nutation in the fluid core is known to amplify the forced nutations in the near-diurnal retrograde frequency band (as measured in the planetary frame of reference). Due to their proximity in shape and frequency, this mode is sometimes equated with the so-called spin-over mode, which denotes the free oscillation of a steadily rotating ellipsoidal fluid core. Through a careful study of the freely rotating two-layer planetary model with a rigid mantle and an inviscid fluid core, we show that the spin-over mode frequency corresponds to that where the sum of the external and internal torques on the mantle is balanced, causing it to rotate steadily. The presence of dissipation at the core−mantle boundary causes the free core nutation to become damped and slightly offsets its resonance frequency. We show that this offset, which is ≈−1 day for Earth, can be interpreted as the result of the proximity of the free core nutation frequency to that of the spin-over mode, which now corresponds to a minimum in the magnitude of the transfer function for nutations. We also show how this proximity leads to a slightly lower quality factor for the resonance than that computed from the usual formula. We conclude by discussing possible implications of this mechanism for Mars, the Moon, and the long-term evolution of Earth.

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“…Improved seismic equipment on the Moon may eventually give the densities of the lunar inner and outer cores and hence constrain its concentration of S. Currently, lunar libration data do not provide useful constrains on lunar core density [ Barkin et al ., ; Williams and Boggs , ]. The presence or absence of any molten silicates in the deep Moon is another constraint.…”

Section: Minor and Trace Elementsmentioning

confidence: 99%

Asteroid bombardment and the core of Theia as possible sources for the Earth's late veneer component

Sleep

2016

Geochem Geophys Geosyst

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The silicate Earth contains Pt-group elements in roughly chondritic relative ratios, but with absolute concentrations <1% chondrite. This veneer implies addition of chondritelike material with 0.3-0.7% mass of the Earth's mantle or an equivalent planet-wide thickness of 5-20 km. The veneer thickness, 200-300 m, within the lunar crust and mantle is much less. One hypothesis is that the terrestrial veneer arrived after the moon-forming impact within a few large asteroids that happened to miss the smaller Moon.Alternatively, most of terrestrial veneer came from the core of the moon-forming impactor, Theia. The Moon then likely contains iron from Theia's core. Mass balances lend plausibility. The lunar core mass is ~1.6×10 21 kg and the excess FeO component in the lunar mantle is 1.3-3.5×10 21 kg as Fe, totaling 3-5×10 21 kg or a few percent of Theia's core. This mass is comparable to the excess Fe of 2.3-10×10 21 kg in the Earth's mantle inferred from the veneer component. Chemically in this hypothesis, Fe metal from Theia's core entered the Moon-forming disk. H 2 O and Fe 2 O 3 in the disk oxidized part of the Fe, leaving the lunar mantle near a Fe-FeO buffer. The remaining iron metal condensed, gathered Pt-group elements eventually into the lunar core. The silicate Moon is strongly depleted in Pt-group elements. In contrast, the Earth's mantle contained excess oxidants, H 2 O and Fe 2 O 3 , which quantitatively oxidized the admixed Fe from Theia's

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Effects of a physical librations of the moon caused by a liquid core, and determination of the fourth mode of a free libration

Cited by 12 publications

References 8 publications

Free Core Nutation and its relation to the Spin-Over Mode

Free Core Nutation and its relation to the Spin-Over Mode

Free Core Nutation and Its Relation to the Spin-over Mode

Asteroid bombardment and the core of Theia as possible sources for the Earth's late veneer component

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