标题： 月球内核的卡西尼状态 显示英文标题

标题： The Cassini State of the Moon's inner core

摘要： 我们提出了一种包含流体外核和固体内核的月球进动动力学模型。我们表明，与内核相关的存在三个卡西尼状态。这些状态下内核的倾斜角度由自由内核章动频率（$\omega_{ficn}$）与进动频率$\Omega_p = 2\pi/18.6$年$^{-1}$的比率决定。如果$|\omega_{ficn}| > 2\pi/16.4$年$^{-1}$，则这三个卡西尼状态都是可能的，但否则只有一个是可能的。假设最低能量状态是最有利的，这一转变标志着内核倾斜角度的不连续性，从相对于地幔轴线的$-33^\circ$转变为$17^\circ$，负角度表示向轨道法线倾斜。 可能的月球内部密度结构范围从大约$\omega_{ficn}$到大约是$\Omega_p$一倍半到两倍，因此内核的确切倾斜角度仍然是未知的，尽管由于$\Omega_p$处于$\omega_{ficn}$的共振带内，它可能是较大的。采用一个特定的密度模型，我们建议内核的倾斜角度约为$-17^\circ$。内核内部的粘弹性变形以及倾斜内核表面的熔化和生长，在我们的模型中都被忽略了，这些因素应该会减小这个幅度。如果内核大于大约200公里，它可能会对$1.543^\circ$观测到的地幔进动角度产生多达几千分之一度的影响。 显示英文摘要

摘要： 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 ($\omega_{ficn}$) and the precession frequency $\Omega_p = 2\pi/18.6$ yr $^{-1}$. All three Cassini states are possible if $|\omega_{ficn}| > 2\pi/16.4$ yr $^{-1}$, but only one is possible otherwise. Assuming that the lowest energy state is favoured, this transition marks a discontinuity in the tilt angle of the inner core, transiting from $-33^\circ$ to $17^\circ$ as measured with respect to the mantle figure axis, where negative angles indicate a tilt towards the orbit normal. Possible Lunar interior density structures cover a range of $\omega_{ficn}$, from approximately half to twice as large as $\Omega_p$, so the precise tilt angle of the inner core remains unknown, though it is likely large because $\Omega_p$ is within the resonant band of $\omega_{ficn}$. Adopting one specific density model, we suggest an inner core tilt of approximately $-17^\circ$. 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 $1.543^\circ$.