On the Origin of Commensurabilities in the Solar System--I The Tidal Hypothesis

Abstract

A method of statistically analysing the distribution of mean motions in the solar system is developed. The results of the analysis suggest that the preference for near-commensurability among pairs of mean motions is a condition of formation rather than the result of evolution. Tidal evolution in the satellite systems of Jupiter, Saturn and Uranus is discussed and it is shown that whilst, in general, no limits can be placed on the dissipative function, Q^–1 , it is probable that tides have produced only small changes in the mean motions of the satellites.