A De Broglie-Like Wave in the Planetary Systems

TL;DR

This paper proposes a semi-accurate de Broglie-like wave model for planetary systems that reproduces the Titius-Bode-Richardson rule, suggesting planets' orbits are sums of natural numbers of wave types.

Contribution

It introduces a novel semi-accurate de Broglie-like wave approach to planetary systems, extending prior quantum-like models with interference phenomena.

Findings

Reproduces Titius-Bode-Richardson rule using wave model

Shows planetary orbits as sums of wave-based natural numbers

Proposes interference phenomena in planetary orbit formation

Abstract

In this work we do an "interpolation" of Scardigli theory of a quantum-like description of the planetary system that reproduces remarkable Titius-Bode-Richardson rule. More precisely, instead of simple, approximate, Bohr-like theory, or, accurate, Schr$\ddot{o}$dinger-like theory, considered by Scardigli, we suggest originally a semi-accurate, de Broglie-like description of the planetary system. Especially, we shall propose a de Broglie-like waves in the planetary systems. More precisely, in distinction from Scardigly (which postulated absence of the interference phenomena at planet orbits) we shall prove that, roughly speaking, planets orbits equal a sum of natural numbers of two types, large and small, of the de-Broglie-like waves. It is similar to well-known situation in atomic physics by interpretation of Bohr momentum quantization postulate by de Broglie relation.