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

TL;DR

This paper explores harmonic and mirror symmetries in the solar system's planetary distances, proposing a musical-inspired model that predicts asteroid gaps and planetary ratios with high accuracy.

Contribution

It introduces a novel mathematical framework inspired by music theory to describe the structure and self-organization of the solar system's planetary distances.

Findings

Model predicts asteroid Kirkwood gaps with 99% accuracy

Reveals mirror symmetries related to harmonic ratios among planets

Suggests planetary organization influenced by Jupiter's resonances

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.