Submitted:
31 January 2019
Posted:
31 January 2019
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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
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