Preprint Article Version 2 This version is not peer-reviewed

Classical and Quantum Kepler's Third Law of N-Body System

Version 1 : Received: 14 December 2018 / Approved: 17 December 2018 / Online: 17 December 2018 (16:21:55 CET)
Version 2 : Received: 31 January 2019 / Approved: 31 January 2019 / Online: 31 January 2019 (11:52:22 CET)

A peer-reviewed article of this Preprint also exists.

Sun, B. Classical and Quantum Kepler's Third Law of N-Body System. Results in Physics 2019, 13, 102144 Sun, B. Classical and Quantum Kepler's Third Law of N-Body System. Results in Physics 2019, 13, 102144

Journal reference: Results in Physics 2019, 13, 102144
DOI: 10.1016/j.rinp.2019.02.080

Abstract

Inspired by amazing result obtained by Semay [1], this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication [2] but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: Tq|Eq|3/2 = πG/√2[(ΣNi=1 ΣNj=i+1 mimj)3/(ΣNk=1 mk)]1/2. This formulae is, of course, consistent with the Kepler's third law of 2-body system, and exact same as Semay's quantum result for identical bodies.

Subject Areas

Kepler's third law; n-body system; periodic orbits; dimensional analysis, classical and quantum mechanics

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