The Darwin-Kaula theory of bodily tides is intended for celestial bodies in nonresonant spin states, as well as for bodies in spin-orbit resonances with no libration. We demonstrate that this theory, in its customary form, is inapplicable to a body caught in a spin-orbit resonance and librating in it. Specifically, in the presence of libration, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin-Kaula theory for a non-librating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration.
We derive the tidal spectrum for longitudinal libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the triaxiality-caused torque; so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality.
Finally, we calculate the tidal dissipation rate in a body experiencing forced libration in longitude.
J. Frouard and M. Efroimsky
Mon, 27 Feb 17