Commensurability and Molchanov's hypothesis

M. B. Gubaidullin

Faculty of Mathematics and Information Technologies, Federal State Budget Educational Organization of Higher Professional Education Bashkir State University, Ufa, Russia

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.

Keywords: resonance, commensurability.

PACS: 96.12.De

MSC: 70E55

Received: 09.06.2015
Revised: 02.10.2015

DOI: 10.4213/tmf8986

 English version: Theoretical and Mathematical Physics, 2016, 187:1, 570–582

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