Orbital Period Ratios and Fibonacci Numbers in Solar Planetary and Satellite Systems and in Exoplanetary Systems

TL;DR

This paper demonstrates that orbital period ratios in various planetary systems tend to align with ratios of Fibonacci numbers, especially with smaller integers, suggesting a potential underlying mathematical pattern in orbital resonances.

Contribution

It reveals a statistical preference for Fibonacci-based ratios in orbital periods across multiple planetary systems and provides a simple model explaining the strength of these resonances.

Findings

Approximately 60% of period ratios are near Fibonacci fractions.

Proximity to Fibonacci ratios increases with smaller inclinations and eccentricities.

A model explains why ratios of small integers are more common in orbital resonances.

Abstract

It is shown that orbital period ratios of successive secondaries in the Solar planetary and giant satellite systems and 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% to 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 resonances with ratios of orbital periods $P_{1}$ and $P_{2}$ of successive secondaries being equal to ratio of small integers $p$ and $(p+q)$, $P_{1}/P_{2}=p/(p+q)$, are stronger and more commonly observed.