Bodily tides near spin–orbit resonances
Bodily tides near spin–orbit resonances
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DOI：
10.1007/s10569-011-9397-4
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发表时间：
2011-05
影响因子：
1.6
通讯作者：
M. Efroimsky
中科院分区：
文献类型：
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作者：
M. Efroimsky
自旋轨道耦合可以用两种方法来描述。第一种方法，称为“麦克唐纳转矩”，通常与一个方便的假设相结合，即品质因数Q与频率无关。这使得方法不一致，因为麦克唐纳扭矩表达式的推导通过将Q标度作为潮汐频率的倒数而默认地固定了地幔的流变学。自旋-轨道耦合也可以用称为“达尔文力矩”的方法来处理。虽然这一理论是普遍的，足以容纳一个任意的频率依赖性ofQ，这一优势尚未得到充分利用的文献中，其中Q是经常假设常数或设置为逆潮汐频率的比例，后者的断言使达尔文扭矩相当于一个修正版本的麦克唐纳扭矩。然而，无论是常数还是逆频率Q都不能反映实际地幔和结壳的性质，因为实际的频率依赖性更复杂。因此，有必要用正确的频率依赖性来丰富自旋轨道相互作用理论。我们完成了这个方案的达尔文扭矩为基础的模型附近的共振。我们从固体力学的第一原理推导出潮汐扭矩的频率依赖性，即，从时间域中的地幔顺应性的表达式。我们还解释了潮汐扭矩不仅包括习惯的，长期的一部分，但也振荡的一部分。我们证明，当次级穿过引潮力共振时，潮汐力矩的Darwin-Kaula展开的引潮力项平滑地通过零（例如，当次级潮汐力矩穿过同步轨道时，主潮汐力矩平稳地通过n1）。因此，我们准备了一个基础的建模诱捕的一个初级到共振与其次级。可以扮演主要和次要的角色，例如，水星和太阳，或者是一个冰冷的月亮和一个木星。我们还提供了一个可能的解释，在月球上的潮汐耗散率的“不当”的频率依赖性，发现LLR。
Spin–orbit coupling can be described in two approaches. The first method, known as the“MacDonald torque”, is often combined with a convenient assumption that the quality factorQis frequency-independent. This makes the method inconsistent, because derivation of the expression for the MacDonald torque tacitly fixes the rheology of the mantle by makingQscale as the inverse tidal frequency. Spin–orbit coupling can be treated also in an approach called“the Darwin torque”. While this theory is general enough to accommodate an arbitrary frequency-dependence ofQ, this advantage has not yet been fully exploited in the literature, whereQis often assumed constant or is set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent to a corrected version of the MacDonald torque. However neither a constant nor an inverse-frequencyQreflect the properties of realistic mantles and crusts, because the actual frequency-dependence is more complex. Hence it is necessary to enrich the theory of spin–orbit interaction with the right frequency-dependence. We accomplish this programme for the Darwin-torque-based model near resonances. We derive the frequency-dependence of the tidal torque from the first principles of solid-state mechanics, i.e., from the expression for the mantle’s compliance in the time domain. We also explain that the tidal torque includes not only the customary, secular part, but also an oscillating part. We demonstrate that thelmpqterm of the Darwin–Kaula expansion for the tidal torque smoothly passes zero, when the secondary traverses thelmpqresonance (e.g., the principal tidal torque smoothly goes through nil as the secondary crosses the synchronous orbit). Thus, we prepare a foundation for modeling entrapment of a despinning primary into a resonance with its secondary. The roles of the primary and secondary may be played, e.g., by Mercury and the Sun, correspondingly, or by an icy moon and a Jovian planet. We also offer a possible explanation for the “improper” frequency-dependence of the tidal dissipation rate in the Moon, discovered by LLR.