Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
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 t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2022-01-01
|
| Series: | Frontiers in Astronomy and Space Sciences |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fspas.2021.758184/full |
| _version_ | 1798026023321731072 |
|---|---|
| author | Michael J. Bank Nicola Scafetta |
| author_facet | Michael J. Bank Nicola Scafetta |
| author_sort | Michael J. Bank |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T18:28:32Z |
| format | Article |
| id | doaj.art-3d9cd8843d394eac914149f94904c741 |
| institution | Directory Open Access Journal |
| issn | 2296-987X |
| language | English |
| last_indexed | 2024-04-11T18:28:32Z |
| publishDate | 2022-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Astronomy and Space Sciences |
| spelling | doaj.art-3d9cd8843d394eac914149f94904c7412022-12-22T04:09:31ZengFrontiers Media S.A.Frontiers in Astronomy and Space Sciences2296-987X2022-01-01810.3389/fspas.2021.758184758184Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar SystemMichael J. Bank0Nicola Scafetta1Danbury Music Centre, Danbury, CT, United StatesDepartment of Earth Sciences, Environment and Georesources, University of Naples Federico II, Complesso Universitario di Monte S. Angelo, Naples, ItalyOrbital 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.https://www.frontiersin.org/articles/10.3389/fspas.2021.758184/fullsolar systemorbital self-organizationorbital symmetriesorbital resonancesmusic and astronomy |
| spellingShingle | Michael J. Bank Nicola Scafetta Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System Frontiers in Astronomy and Space Sciences solar system orbital self-organization orbital symmetries orbital resonances music and astronomy |
| title | Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System |
| title_full | Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System |
| title_fullStr | Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System |
| title_full_unstemmed | Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System |
| title_short | Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System |
| title_sort | scaling mirror symmetries and musical consonances among the distances of the planets of the solar system |
| topic | solar system orbital self-organization orbital symmetries orbital resonances music and astronomy |
| url | https://www.frontiersin.org/articles/10.3389/fspas.2021.758184/full |
| work_keys_str_mv | AT michaeljbank scalingmirrorsymmetriesandmusicalconsonancesamongthedistancesoftheplanetsofthesolarsystem AT nicolascafetta scalingmirrorsymmetriesandmusicalconsonancesamongthedistancesoftheplanetsofthesolarsystem |