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In geophysics and seismology, it is a common knowledge that the quality factors Q of the mantle and crust materials scale as the tidal frequency to a positive fractional power (Karato 2007, Efroimsky and Lainey 2007). In astronomy, there exists an equally common belief that such rheological models introduce discontinuities into the equations and thus are unrealistic at low frequencies. We demonstrate that, while such models indeed make the conventional expressions for the tidal torque diverge for vanishing frequencies, the emerging infinities reveal not the impossible nature of one or another rheology, but a subtle flaw in the underlying mathematical model of friction. Flawed is the common misassumption that the tidal force and torque are inversely proportional to the quality factor. In reality, they are proportional to the sine of the tidal phase lag, while the inverse quality factor is commonly identified with the tangent of the lag. The sine and tangent of the lag are close everywhere {it{except in the vicinity of the zero frequency}}. Reinstating of this detail tames the fake infinities and rehabilitates the impossible scaling law (which happens to be the actual law the mantles obey). This preprint is a pilot paper. A more comprehensive treatise on tidal torques is to be published (Efroimsky and Williams 2009).
We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates correcti
We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such configurations was
Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies tidal despinning, and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directl
Stellar radiation has conservatively been used as the key constraint to planetary habitability. We review here the effects of tides, exerted by the host star on the planet, on the evolution of the planetary spin. Tides initially drive the rotation pe
We present a method for decomposing the cosmological velocity field in a given volume into its divergent component due to the density fluctuations inside the volume, and its tidal component due to the matter distribution outside the volume. The input