The Physics of Bodily Tides in Terrestrial Planets, and the Appropriate Scales of Dynamical Evolution

By M. Efroimsky, V. Lainey. 2007

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Any model of tides is based on a specific hypothesis of how lagging depends on the tidal-flexure frequency. For example, Gerstenkorn (1955), MacDonald (1964), and Kaula (1964) assumed constancy of the geometric lag angle, while Singer (1968) and Mignard (1979, 1980) asserted constancy of the time lag. Thus, each of these two models was based on a certain law of scaling of the geometric lag. 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. Since at present we know the shape of the dependence of Q upon the frequency, we can reverse our line of reasoning and single out the appropriate actual frequency-dependence of the angular lag. This dependence turns out to be different from those employed hitherto, and it entails considerable alterations in the time scales of the tide-generated dynamical evolution. Phobos' fall on Mars is an example we consider.

Subfields: Astronomy and Astrophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/44ebfb22a4975dac7a9986372d2af3c2e46c5070

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Citations in the corpus

Bodily tides near spin–orbit resonances (2011, background): “Stated alternatively, the tidal Q is not much different from the seismic Q (up to an insignificant rescaling due to self-gravity – see an estimate in section 3.4 of Efroimsky & Lainey 2007).”
Tidal obliquity evolution of potentially habitable planets (2011, background): “107 Hz (Efroimsky & Lainey 2007b,a).”
Tidal torques: a critical review of some techniques (2008, methodology): “m=0 (l − m)! (l + m)! (2 − δ0m) Plm(sin φ) Plm(sin φ) cos m(λ − λ) , (13) substitution whereof into (11) results in W ( ~ R , ~r ) = − G M ∗ sat r ∗ ∞”
TIDALLY HEATED TERRESTRIAL EXOPLANETS: VISCOELASTIC RESPONSE MODELS (2009, background): “…dissipation measurements from Earth’s Chandler wobble, tides and free oscillations, summarized in Karato & Spetzler (1990) show Q values which change gradually with frequency, and are modeled well by empirical power laws of the form Q ∼ ωαQ (αQ = 0.1 to 0.4) (Karato 2007; Efroimsky & Lainey 2007).”
ORBITS AND MASSES OF THE SATELLITES OF THE DWARF PLANET HAUMEA (2003 EL61) (2009, background): “In other words, if Qp is frequency dependent (as it seems to be for solid bodies, see Efroimsky & Lainey 2007)), then an effective Q of ∼16 may be equivalent to an object with a one-day rotation period maintaining an effective Q of 100, the typically assumed value for icy solid bodies.”