On the Origin of Commensurabilities in the Solar System--II The Orbital Period Relation

Abstract

A systematic search for regularity in the major satellite systems has revealed that the orbital periods of the regular satellites are closely approximated by the relation, $${T}_{n}\,=\,{T}_{0}{A}^{n}\,\text{where}\,{T}_{n}$$ is the orbital period of the n th satellite. It must be allowed though, that in any one system there are a small number of vacancies. For all systems A is the square root of a small integer and it is suggested that T₀ is related to the rotational period of the primary. The relation can be applied to the planetary system but there are some anomalies. It is suggested that this regularity, which is related to the preference for near-commensurability among pairs of mean motions in the solar system, is a condition of formation rather than the result of evolution and thus could be of considerable cosmogonic importance.