Analyses of Lunar Laser Ranging data show that the spin symmetry axis of the Moon is ahead of its expected Cassini state by an angle of ϕ _p = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid‐body tides and viscous core‐mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the center of the Moon can also account for a part of the observed phase lead angle ϕ _p . We build a rotational dynamic model of the Cassini state of the Moon that comprises an inner core, a fluid core, and a mantle and where solid regions are allowed to deform viscoelastically in response to an applied forcing. We show that the presence of an inner core does not change the global monthly Q of the Moon and, hence, that the contribution from solid‐body tides to ϕ _p is largely unaffected by an inner core. However, we also show that viscoelastic deformation within the inner core, acting to realign its figure axis with that of the mantle, can contribute significantly to ϕ _p through inner core‐mantle gravitational coupling. We show that the contribution to ϕ _p is largest when the inner core viscosity is in the range of 10¹³ to 10¹⁴ Pa s, when the inner core radius is large and when the free inner core nutation frequency approaches a resonance with the precession frequency of 2π /18.6 yr⁻¹.

中文翻译：

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月球内的粘弹性弛豫及其卡西尼状态的相线

对月球激光测距数据的分析表明，月球的自旋对称轴比其预期的卡西尼状态提前了一个ϕ _p = 0.27 arcsec的角度。这表明存在一个或多个作用于月球旋转的耗散机制。在以前的研究中已经提出了固体潮汐和粘性芯-幔耦合的组合。在这里，我们研究在月球中心的固体内核内部的粘弹性变形是否也可以解释所观测到的相位超前角ϕ _{p的一部分}。我们建立了卡西尼号月球状态的旋转动力学模型，该模型包括一个内芯，一个流体芯和一个地幔，并允许固体区域响应施加的力而发生粘弹性变形。我们表明，内核的存在并不会改变全球月球Q值，因此，固体潮汐对ϕ _p的贡献在很大程度上不受内核的影响。然而，我们还显示了内芯内的粘弹性变形，作用于调整其形状轴与地幔的，可以显著有助于φ _p通过内芯幔引力耦合。我们发现，在贡献φ _p是最大的，当内芯粘度为范围10 ¹³到10 ¹⁴ 帕S，当内芯半径大，并且当自由内芯摆动频率接近谐振用的进动频率2 π /18.6 年^-1。