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

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 [Formula: see text]. 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 [Formula: see text] and 16 (14%) with less than [Formula: see text]. 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 [Formula: see text] [Formula: see text]km/s to more than 1,200[Formula: see text]km/s and can be described in terms of a few peaks centered on integer multiple of a super-fundamental speed [Formula: see text] [Formula: see text]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.