Commensurability and Molchanov’s hypothesis

Abstract

About half a century ago, A. M. Molchanov conjectured the existence of a resonance structure of the solar system, stating that as the solar system evolves, its planets inevitably drift to orbits for which the ratios of their orbital periods become close to ratios of relatively small natural numbers. In Molchanov’s opinion, this resonance property is ensured by small dissipative forces. We offer another possible explanation of this phenomenon without taking dissipation into account.