论文标题
月球内部核心的卡西尼状态
The Cassini State of the Moon's inner core
论文作者
论文摘要
我们提出了一个模型的月球动力学模型，该模型包括一个流体外核和固体内核。我们表明，存在与内核相关的三个Cassini状态。这些状态中每个状态中内核的倾斜角度取决于自由的内核营养频率（$ω__{ficn} $）与进动频率$ω_p=2π/18.6 $ yr $^{ - 1} $之间的比率。如果$ |ω__{ficn} | >2π/16.4 $ yr $^{ - 1} $，但否则只有一个。假设最低的能量状态是偏爱的，这种过渡标志着内核的倾斜角度的不连续性，从$ -33^\ circ $到$ 17^\ circ $，如地幔图形轴所测量的，其中负角度表明倾斜倾向于Orbit正常。可能的月球内部密度结构覆盖了$ω_{ficn} $的范围，大约是$ω_p$的一半到两倍，因此内核的精确倾斜角度仍然未知，尽管$ω_p$可能很大，因为$ω_p$在$ω__{ficn}的谐振频段内。采用一个特定的密度模型，我们建议内部核心倾斜约为$ -17^\ circ $。内核内的粘弹性变形，熔融和生长在我们模型中忽略的倾斜内核表面，应降低这种振幅。如果内芯大约大于200公里，则可能会在观察到的套料进料角$ 1.543^\ circ $上贡献多达几千分表。
We present a model of the precession dynamics of the Moon that comprises a fluid outer core and a solid inner core. We show that three Cassini states associated with the inner core exist. The tilt angle of the inner core in each of these states is determined by the ratio between the free inner core nutation frequency ($ω_{ficn}$) and the precession frequency $Ω_p = 2π/18.6$ yr $^{-1}$. All three Cassini states are possible if $|ω_{ficn}| > 2π/16.4$ 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 $ω_{ficn}$, 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 $ω_{ficn}$. 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 $1.543^\circ$.
