Resolution-Scale Relativity signatures in the orbital periods of extra-solar planetary systems

Abstract: Resolution-Scale Relativity suggests quantum-like dynamics may emerge in chaotic macroscopic systems. In planetary systems, this would lead to orbital periods being proportional to cubed integers $n$. Each system is then characterized by a fundamental speed corresponding to orbital $n=1$. Fitting this model to data from the NASA Exoplanet Archive for 115 planetary systems with four or more planets leads to identifying 38 systems (33\%) complying with an accuracy such that the null hypothesis accidental probability is less than $10<sup>{-2}$, and 16 (14\%) with less than $10<sup>{-3}$. Additionally, 34 systems (29\%) follow a pattern of consecutive quantum-like integer numbers, and 101 (88\%) in which at least half of the quantum-like numbers are part of consecutive sequences. The distribution of fundamental speeds extends from $\sim 100\,\rm km/s$ to more than $1,200\,\rm km/s$ and can be described in terms of a few peaks centered on integer multiple of a super-fundamental speed $v_0=(218.0\pm4.7)\,\rm km/s$. These results along side with other observations in turbulent fluid dynamics amount to a shift to a higher gear in the search for macro-quantization effects.