On the Theory of Bodily Tides

Different theories of bodily tides assume different forms of dependence of the angular lag 8 upon the tidal frequency %. In the old theory (Gerstenkorn 1955, MacDonald 1964, Kaula 1964) the geometric lag angle is assumed constant (i.e., 8 ~ x), while the new theory (Singer 1968; Mignard 1979, 1980) postulates constancy of the time lag At (which is equivalent to saying that 8 ~ j} ). Each particular functional form of 8 (%) unambiguously determines the form of the frequency dependence of the tidal quality factor, Q(x)> a n d v i c e versa. Through the past 20 years, several teams of geophysicists have undertaken a large volume of experimental research of attenuation at low frequencies. This research, carried out both for mineral samples in the lab and for vast terrestrial basins, has led to a complete reconsideration of the shape of Q(x)While in late 70s early 80s it was universally accepted that at low frequencies the quality factor scales as inverse frequency, by now it is firmly established that Q ~ x, where the positive fractional power a varies, for different minerals, from 0.2 through 0.4 (leaning toward 0.2 for partial melts) see the paper by Efroimsky (2006) and references therein. That paper also addresses some technical difficulties emerging in the conventional theory of land tides, and offers a possible way of their circumvention a new model that is applicable both for high inclinations and high eccentricities (contrary to the Kaula expansion which converges only for i ^ 7l/2 and e < 0.6627434). Here we employ this new model to explore the long-term evolution of Phobos and to provide a more exact estimate for the time it needs to fall on Mars. This work is a pilot paper that anticipates a more comprehensive study in preparation (Efroimsky & Lainey 2007).