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

TL;DR

This paper investigates the complex frequency dependence of tidal lag in terrestrial planets, revealing that actual rheological properties lead to different dynamical evolution timescales than traditional models suggest.

Contribution

It introduces a revised model for tidal lag based on planetary rheology, altering the understanding of tidal evolution timescales compared to previous assumptions.

Findings

The actual lag dependence differs from traditional models.

Revised lag dependence affects dynamical evolution timescales.

Application to Phobos' fall on Mars illustrates the impact.

Abstract

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.