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Prevalence of Fibonacci numbers in orbital period ratios in solar planetary and satellite systems and in exoplanetary systems

Abstract

It is shown that orbital period ratios of successive planets in the Solar System, of satellites in giant planet systems and of exoplanets in exoplanetary systems are preferentially closer to irreducible fractions formed with Fibonacci numbers between 1 and 8 than to other fractions, in a ratio of approximately 60% vs 40%. Furthermore, if sets of minor planets are chosen with gradually smaller inclinations and eccentricities, the proximity to Fibonacci fractions of their period ratios with Jupiter or Mars’ period tends to increase. Finally, a simple model explains why the resonance of the form \(\frac{P_{1}}{P_{2}} = \frac{p}{p+q}\), with \(P_{1}\) and \(P_{2}\) orbital periods of planets or satellites and \(p\) and \(q\) small integers, are stronger and more commonly observed for \(p\) and \(( p+q )\) being both small Fibonacci numbers than for other cases.

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Acknowledgements

This research has made use of data and/or services provided by the International Astronomical Union’s Minor Planet Center. Prof. D. Huylebrouck and Prof. L. Basano kindly provided comments on early versions of the manuscript. Stimulating discussions with C. Ducrest are also acknowledged.

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Pletser, V. Prevalence of Fibonacci numbers in orbital period ratios in solar planetary and satellite systems and in exoplanetary systems. Astrophys Space Sci 364, 158 (2019). https://doi.org/10.1007/s10509-019-3649-2

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  • DOI: https://doi.org/10.1007/s10509-019-3649-2

Keywords

  • Orbital period ratios
  • Near mean motion resonances
  • Fibonacci numbers
  • Solar System
  • Giant planet satellite systems
  • Minor planets
  • Exoplanetary systems