Inspired by amazing result obtained by Semay \cite{ 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 \cite{ sun2018} but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: $T_q|E_q|^{ 3/2}=\frac{ \pi}{ \sqrt{ 2}} G\left[\frac{ \left(\sum_{ i=1}^N\sum_{ j=i+1}^Nm_im_j\right)^3}{ \sum_{ k=1}^N m_k}\right]^{ 1/2}$. 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.
Categories: physics.gen-ph