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In geophysics and seismology, it is a common knowledge that the qualityfactors Q of the mantle and crust materials scale as the tidal frequency to apositive fractional power (Karato 2007, Efroimsky and Lainey 2007). Inastronomy, there exists an equally common belief that such rheological modelsintroduce discontinuities into the equations and thus are unrealistic at lowfrequencies. We demonstrate that, while such models indeed make theconventional expressions for the tidal torque diverge for vanishingfrequencies, the emerging infinities reveal not the impossible nature of one oranother rheology, but a subtle flaw in the underlying mathematical model offriction. Flawed is the common misassumption that the tidal force and torqueare inversely proportional to the quality factor. In reality, they areproportional to the sine of the tidal phase lag, while the inverse qualityfactor is commonly identified with the tangent of the lag. The sine and tangentof the lag are close everywhere {\it{except in the vicinity of the zerofrequency}}. Reinstating of this detail tames the fake infinities andrehabilitates the "impossible" scaling law (which happens to be the actual lawthe mantles obey). This preprint is a pilot paper. A more comprehensivetreatise on tidal torques is to be published (Efroimsky and Williams 2009).

Can the tidal quality factors of terrestrial planets and moons scale as positive powers of the tidal frequency?