Bodily Tides near the 1:1 Spin-Orbit Resonance: Correction to Goldreich's Dynamical Model.

摘要

Spin-orbit coupling is often described in an approach known as 'the MacDonald torque', which has long become the textbook standard due to its apparent simplicity. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (Rev Geophys 2:467-541, 1964), is combined with a convenient assumption that the quality factor Q is frequency- independent (or, equivalently, that the geometric lag angle is constant in time). This makes the treatment unphysical because MacDonald's derivation of the said formula was, very implicitly, based on keeping the time lag frequency- independent, which is equivalent to setting Q scale as the inverse tidal frequency. This contradiction requires the entire MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky and Williams (Cel Mech Dyn Astron 104:257-289, 2009), in application to spin modes distant from the major commensurabilities.