On the Theory of Bodily Tides
Abstract
Different theories of bodily tides assume different forms of dependence of the angular lag (delta) upon the tidal frequency X (chi). In the old theory (Gerstenkorn 1955, MacDonald 1964, Kaula 1964) the geometric lag angle is assumed constant, while the new theory (Singer 1968; Mignard 1979, 1980) postulates constancy of the time lag (delta)-t. Each particular functional form of delta-X (chi) unambiguously determines the form of the frequency dependence of the tidal quality factor, and vice 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)(chi-alpha), where the positive fractional power alpha 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. 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).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2007
- Accession Number
- ADA465313
Entities
People
- Michael Efroimsky
- Valery Lainey
Organizations
- United States Naval Observatory