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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)
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
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.
Keywords
Kepler's third law; n-body system; periodic orbits; dimensional analysis, classical and quantum mechanics
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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