1105.6086 (Michael Efroimsky)
Michael Efroimsky
Spin-orbit coupling can be described in two approaches. The method known as
"the MacDonald torque" is often combined with an assumption that the quality
factor Q is frequency-independent. This makes the method inconsistent, because
the MacDonald theory tacitly fixes the rheology by making Q scale 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 of Q, this advantage has not yet been exploited in the
literature, where Q is 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-frequency Q reflect the properties
of realistic mantles and crusts, because the actual frequency-dependence is
more complex. Hence the necessity 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, 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 secular part, but also an
oscillating part.
We demonstrate that the lmpq term of the Darwin-Kaula expansion for the tidal
torque smoothly goes through zero, when the secondary traverses the lmpq
resonance (e.g., the principal tidal torque smoothly goes through nil as the
secondary crosses the synchronous orbit).
We also offer a possible explanation for the "improper" frequency-dependence
of the tidal dissipation rate in the Moon, discovered by LLR.
View original:
http://arxiv.org/abs/1105.6086
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