Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System

Abstract

Orbital systems are often self-organized and/or characterized by harmonic relations. Inspired by music theory, we rewrite the Geddes and King-Hele (QJRAS, 24, 10–13, 1983) equations for mirror symmetries among the distances of the planets of the Solar System in an elegant and compact form by using the 2/3rd power of the ratios of the semi-major axis lengths of two neighboring planets (eight pairs, including the belt of the asteroids). This metric suggests that the Solar System could be characterized by a scaling and mirror-like structure relative to the asteroid belt that relates together the terrestrial and Jovian planets. These relations are based on a 9/8 ratio multiplied by powers of 2, which correspond musically to the interval of the Pythagorean epogdoon (a Major Second) and its addition with one or more octaves. Extensions of the same model are discussed and found compatible also with the still hypothetical vulcanoid asteroids versus the transneptunian objects. The found relation also suggests that the planetary self-organization of our system could be generated by the 3:1 and 7:3 resonances of Jupiter, which are already known to have shaped the asteroid belt. The proposed model predicts the main Kirkwood asteroid gaps and the ratio among the planetary orbital parameters with a 99% accuracy, which is three times better than an alternative, recently proposed harmonic-resonance model for the Solar System. Furthermore, the ratios of neighboring planetary pairs correspond to four musical “consonances” having frequency ratios of 5/4 (Major Third), 4/3 (Perfect Fourth), 3/2 (Perfect Fifth) and 8/5 (Minor Sixth); the probability of obtaining this result randomly has a p < 0.001. Musical consonances are “pleasing” tones that harmoniously interrelate when sounded together, which suggests that the orbits of the planets of our Solar System could form some kind of gravitationally optimized and coordinated structure. Physical modeling indicates that energy non-conserving perturbations could drive a planetary system into a self-organized periodic state with characteristics vaguely similar of those found in our Solar System. However, our specific finding suggests that the planetary organization of our Solar System could be rather peculiar and based on more complex and unknown dynamical structures.

On the Slow Drift of Solstices: Milankovic Cycles and Mean Global Temperature

“…This is a case of agreement between observations and a mathematical formulation. This new finding joins a host of recent results that argue in the same direction Bank et Scafetta (2022); the hypothesis proposes that a forcing by the giant Jovian planets is exerted on a vast number of solar and terrestrial phenomena, including as shown in this paper global surface temperature. This forcing induces a number of responses from the Earth's rotation axis, hence on climate at many time scales.…”

“…It has recently been shown, based on observations, that the Jovian planets exert perturbations both on Earth and in the Sun at much shorter periods (centuries to years and less) (eg. Mörth et Schlamminger (1979); Courtillot et al (2021); Lopes et al (2021b); Bank et Scafetta (2022); Scafetta et Bianchini (2022); Yndestad (2022)).…”

The Planetary Theory of Solar Activity Variability: A Review

“…We have shown that the high synchronization of our own planetary system is nicely revealed by the fact that the ratios of the orbital radii of adjacent planets, when raised to the 2/3rd power, express the simple ratios found in harmonic musical consonances while those of the mirrored ones follow the simple, elegant, and highly precise scaling-mirror symmetry Eq. 1 (Bank and Scafetta, 2022).…”

“…This property is rather common for many orbital systems (Moons and Morbidelli, 1995;Scafetta, 2014a;Aschwanden, 2018;Agol et al, 2021). Bank and Scafetta (2022) improved the Geddes and King-Hele equations describing the mirror symmetries among the orbital radii of the planets (Geddes and King-Hele, 1983) and discovered their ratios obey the following scaling-mirror symmetry relation ≈ 1 a 7:3 a 3:1 2 3 ≈ 9 8…”

“…Due to the evident high synchronization of planetary motions, it is worthwhile investigating the possibility that orbital frequencies could tune solar variability as well. However, although Jupiter appears to play the main role in organizing the solar system (Bank and Scafetta, 2022), its orbital period (~11.86 years) is too long to fit the Schwabe 11-year solar cycle. Thus, any possible planetary mechanism able to create this solar modulation must involve a combination of more planets.…”