Physics of Bodily Tides in Terrestrial Planets and the Appropriate Scales of Dynamical Evolution
Abstract
Any model of tides is based on a specific hypothesis of how lagging depends on the tidal-flexure frequency X. For example, Gerstenkorn (1955), MacDonald (1964), and Kaula (1964) assumed constancy of the geometric lag angle delta, while Singer (1968) and Mignard (1979, 1980) asserted constancy of the time lag Delta t. Thus each of these two models was based on a certain law of scaling of the geometric lag: the Gerstenkorn-MacDonald-Kaula theory implied that delta~X(0), while the Singer-Mignard theory postulated delta~X(1). The actual dependence of the geometric lag on the frequency is more complicated and is determined by the rheology of the planet. Besides, each particular functional form of this dependence will unambiguously fix the appropriate form of the frequency dependence of the tidal quality factor, Q(X). Since at present we know the shape of the function Q(X), we can reverse our line of reasoning and single out the appropriate actual frequency dependence of the lag, delta(X): as within the frequency range of our concern Q ~ X(alpha), a = 0.2 - 0.4, then delta ~ X(-alpha). This dependence turns out to be different from those employed hitherto, and it entails considerable alterations in the timescales of the tide-generated dynamical evolution. Phobos's fall on Mars is an example we consider.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 29, 2007
- Accession Number
- ADA477918
Entities
People
- Michael Efroimsky
- Valery Lainey
Organizations
- United States Naval Observatory