Project “The Moon – 2012+”: Spin-orbital evolution, geophysics and selenodesy of the Moon

Gusev, Alexander; Petrova, Natalia

doi:10.1016/j.asr.2007.06.023

Cited by 3 publications

(5 citation statements)

References 24 publications

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“…Our computed FICN periods are very different from the values of 515 to 635 years reported by Gusev and Petrova [] based on the model of Getino et al []. We attribute this large difference to the fact that, as a cursory look of the expressions of the free modes given in Getino et al [] reveal, their model fails to include properly the gravitational torque from the rest of the Moon acting on a tilted inner core.…”

Section: Resultscontrasting

confidence: 99%

“…This corresponds to a FCN period (in a space‐fixed frame) of approximately ∼375 years. This is slightly longer, though similar, to the FCN period reported in Gusev and Petrova [] and Williams et al [].…”

Section: Resultssupporting

confidence: 85%

“…The period of the FCN gives the timescale by which the fluid core can adjust to a change in the orientation of the mantle. For a small core,

Ā / Ā_{m} \approx 1

, and taking the dynamical ellipticity of the fluid core to be the same as that of the whole Moon, e f =5.18·10 −4 , gives an estimate of the FCN frequency for the Moon of −1.38·10 −9 s −1 (in a space‐fixed frame), or a period of ∼145 years, similar to the value computed in Gusev and Petrova []. Because the ellipticity of the fluid core is likely smaller than that of the whole Moon, the FCN period should be longer than this simple estimate.…”

Section: Theorysupporting

confidence: 71%

“…For Earth, this rotational mode is called the free core nutation (FCN), and we use this terminology here. The FCN period of the Moon is not known but estimated to be longer than ∼150 years [e.g., Gusev and Petrova , ; Williams et al , ], much longer than the 18.6 year period of mantle precession. This implies that the fluid core does not have time to adjust to the precession motion of the mantle and is not efficiently entrained.…”

Section: Introductionmentioning

confidence: 99%

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The forced precession of the Moon's inner core

Dumberry

Wieczorek

2016

JGR Planets

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The tilt angle of the 18.6 year precession of the Moon's solid inner core is unknown, but it is set by a balance between gravitational and pressure torques acting on its elliptical figure. We show here that to first order, the angle of precession of the inner core of a planetary body is determined by the frequency of the free inner core nutation, ωficn, relative to the precession frequency, Ωp. If |ωficn|≪|Ωp|, the inner core is blind to the gravitational influence of the mantle. If |ωficn|≫|Ωp|, the inner core is gravitationally locked to the mantle and is nearly aligned with it. If ωficn≈Ωp, large inner core tilt angles can result from resonant excitation. Viscous inner core relaxation and electromagnetic coupling can attenuate large tilt angles. For the specific case of the Moon, we show that ωficn is to within a factor of 2 of Ωp = 2π/18.6 yr−1. For a rigid inner core, this implies a tilt of 2 to 5° with respect to the mantle, and larger if ωficn is very close to Ωp. More modest tilt angles between 0 and 0.5° result if viscous relaxation within the inner core occurs on a timescale of one lunar day. Predictions from our model may be used in an attempt to detect the gravity signal resulting from a tilted inner core, to determine the past history of the inner core tilt angle, and to assess models of dynamo generation powered by differential rotation at the core‐mantle and inner core boundaries.

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Section: Resultscontrasting

confidence: 99%

Section: Resultssupporting

confidence: 85%

“…The period of the FCN gives the timescale by which the fluid core can adjust to a change in the orientation of the mantle. For a small core,

Ā / Ā_{m} \approx 1

Section: Theorysupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The forced precession of the Moon's inner core

Dumberry

Wieczorek

2016

JGR Planets

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“…The period of the FCN, as seen in the inertial frame, is estimated to be longer than 150 years (e.g., Gusev & Petrova, ; Williams, Boggs, & Ratcliff, ), implying that the fluid core is not efficiently entrained by the 18.6‐year mantle precession. The rotation vector of the fluid core should therefore remain in close alignment with the normal to the ecliptic (e.g., Goldreich, ; Meyer & Wisdom, ; Poincaré, ).…”

Section: Introductionmentioning

confidence: 99%

The Cassini State of the Moon's Inner Core

Stys

Dumberry

2018

JGR Planets

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We present a model of the precession dynamics of the Moon that comprises a fluid outer core and a solid inner core. We show that three Cassini states associated with the inner core exist. The tilt angle of the inner core in each of these states is determined by the ratio between the free inner core nutation frequency ( ficn ) and the precession frequency Ω p = 2 ∕18.6 year −1 . All three Cassini states are possible if | ficn | > 2 ∕16.4 year −1 , but only one is possible otherwise. Assuming that the lowest energy state is favored, this transition marks a discontinuity in the tilt angle of the inner core, transiting from −33 ∘ to 17 ∘ as measured with respect to the mantle figure axis, where negative angles indicate a tilt toward the orbit normal. Possible Lunar interior density structures cover a range of ficn , from approximately half to twice as large as Ω p , so the precise tilt angle of the inner core remains unknown, though it is likely large because Ω p is within the resonant band of ficn . Adopting one specific density model, we suggest an inner core tilt of approximately −17 ∘ . Viscoelastic deformations within the inner core and melt and growth at the surface of a tilted inner core, both neglected in our model, should reduce this amplitude. If the inner core is larger than approximately 200 km, it may contribute by as much as a few thousandths of a degree on the observed mantle precession angle of 1.543 ∘ . Plain Language SummaryIt is well known that the reason we see only one face of the Moon is because the period of its revolution around Earth is equal to the period of Moon's rotation around itself. Yet the full description of the Moon's rotation is a bit more complex. The Lunar spin axis is inclined by 1.54 ∘ in space, and its direction is precessing, like a spinning top, at a period of 18.6 years. This precession is caused by the precession of the plane of the Lunar orbit at the same period, an arrangement known as a Cassini state, named after the seventeenth century Italian astronomer. Like the Earth, the Moon is suspected to have a metallic iron core, its outer region being fluid but the central part being solid. In this work, we calculate the tilt of the spin axis of this solid inner core so that it obeys a Cassini state. We show that this angle can be large, 17 ∘ with respect to the mantle for one specific model but that it is also very sensitive to the specific size and mass of the solid and fluid parts of the Lunar core which are not well known.

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Insight-building models for lunar range and range rate

Williams

2018

Celest Mech Dyn Astr

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Project “The Moon – 2012+”: Spin-orbital evolution, geophysics and selenodesy of the Moon

Cited by 3 publications

References 24 publications

The forced precession of the Moon's inner core

The forced precession of the Moon's inner core

The Cassini State of the Moon's Inner Core

Insight-building models for lunar range and range rate

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