2007/12/06 by Michael Efroimsky, Efroimsky, Michael
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Astro and Planetary Science #Astronomy #Astrophysics #Astrophysics (astro-ph) #Classical Physics (physics.class-ph) #Classical mechanics #Classification of discontinuities #Computer science #Crust #Dissipation factor #Electrical engineering #Engineering #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Geophysics #Geophysics (physics.geo-ph) #Geophysics and Gravity Measurements #Inverse trigonometric functions #Lag #Mathematical analysis #Mathematics #Phase lag #Physics #Planet #Planetary Science and Exploration #Preprint #Quality (philosophy) #Quantum mechanics #Scale (ratio) #Statistical Mechanics and Entropy #Superposition principle #Tangent #Theoretical physics #Tidal power #Torque #astro-ph #physics.class-ph #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.0712.1056
published in arXiv (Cornell University) (Cornell University) · arXiv admin note: text overlap with arXiv:astro-ph/0605521
openalex publication_date 2007/12/06 · arxiv created 2012/02/27 · arxiv updated 2012/03/19 · openalex created_date 2022/09/14 · openalex updated_date 2026/08/05
In geophysics and seismology, it is a common knowledge that the quality\nfactors Q of the mantle and crust materials scale as the tidal frequency to a\npositive fractional power (Karato 2007, Efroimsky and Lainey 2007). In\nastronomy, there exists an equally common belief that such rheological models\nintroduce discontinuities into the equations and thus are unrealistic at low\nfrequencies. We demonstrate that, while such models indeed make the\nconventional expressions for the tidal torque diverge for vanishing\nfrequencies, the emerging infinities reveal not the impossible nature of one or\nanother rheology, but a subtle flaw in the underlying mathematical model of\nfriction. Flawed is the common misassumption that the tidal force and torque\nare inversely proportional to the quality factor. In reality, they are\nproportional to the sine of the tidal phase lag, while the inverse quality\nfactor is commonly identified with the tangent of the lag. The sine and tangent\nof the lag are close everywhere itexcept in the vicinity of the zero\nfrequency. Reinstating of this detail tames the fake infinities and\nrehabilitates the "impossible" scaling law (which happens to be the actual law\nthe mantles obey). This preprint is a pilot paper. A more comprehensive\ntreatise on tidal torques is to be published (Efroimsky and Williams 2009).\n