Tidal friction in closein satellites and exoplane

Authors: Sylvio FerrazMello Adrián Rodríguez Hauke Hussmann

Publish Date: 2008/05/07

Volume: 101, Issue: 1-2, Pages: 171-201

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Abstract

This report is a review of Darwin’s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves except that equal frequency harmonics are assumed to span equal lags Emphasis is given to the cases of companions having reached one of the two possible final states 1 the supersynchronous stationary rotation resulting from the vanishing of the average tidal torque 2 capture into the 11 spinorbit resonance true synchronization In these cases the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period instead of the semidiurnal tide and the singularity due to the vanishing of the geometric phase lag does not exist It is also shown that the true synchronization with nonzero eccentricity is only possible if an extra torque exists opposite to the tidal torque The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion The results are modeldependent and the theory is developed only to the second degree in eccentricity and inclination obliquity It can easily be extended to higher orders but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known

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