  Lunar laser ranging (LLR) data and Apollo seismic data analyses, revealed
independent evidence for the presence of a fluid lunar core. However, the size
of the lunar fluid core remained uncertain by $\pm55$ km (encompassing two
contrasting 2011 Apollo seismic data analyses). Here we show that a new
description of the lunar interior's dynamical model provides a determination of
the radius and geometry of the lunar core-mantle boundary (CMB) from the LLR
observations. We compare the present-day lunar core oblateness obtained from
LLR analysis with the expected hydrostatic model values, over a range of
previously expected CMB radii. The findings suggest a core oblateness
($f_c=(2.2\pm0.6)\times10^{-4}$) that satisfies the assumption of hydrostatic
equilibrium over a tight range of lunar CMB radii ($\mathcal{R}_{CMB}=381\pm12$
km). Our estimates of a presently-relaxed lunar CMB translates to a core mass
fraction in the range of $1.59-1.77\%$ with a present-day Free Core Nutation
(FCN) within $(367\pm100)$ years.
