Commensurability in the solar system

Abstract

The features in common between the well-known Bode–Titius law, other commensurable astronomical relation- ships, and the organization of self-similar atomic systems, are used to demonstrate that the orbital data of all planets, aster- oids, moons and rings in the solar system, reduce to a simple numerical pattern based on the golden ratio. A set of integers, not unlike the quantum numbers of atomic systems define the mean orbits of all planets and major satellites.