论文标题
太阳系行星距离之间的缩放，镜子对称和音乐串扰
Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
论文作者
论文摘要
轨道系统通常是自组织和/或以谐波关系为特征的。受音乐理论的启发，我们通过使用2/3相邻行星的半轴长度（包括八peairs of copt of copters of copters of copt of copters of Music and of音乐理论，Qjras，24，10-13，1983）方程式，通过使用2/3相邻行星的比率的2/3幂的2/3幂，以优雅而紧凑的形式在太阳系行星之间以优雅而紧凑的形式重写。该指标表明，太阳系可以以相对于小行星带相对于陆地和jovian行星的小行星带的缩放和镜面结构来表征。这些关系是基于9/8的比例乘以2的比例，在音乐上对应于毕达哥拉斯的epogdoon的间隔（主要第二个），并与一个或多个八度音阶相对应。讨论了同一模型的扩展，并发现与仍然假设的紫球蛋白小行星相对于跨性别物体兼容。发现的关系还表明，我们系统的行星自组织可以由木星的3：1和7：3产生，木星的共鸣已经塑造了小行星带。提出的模型预测了柯克伍德小行星差距和行星轨道参数之间的比率，精度为99％。
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.
