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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 +/- 55 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 +/- 0.6) x 10(-4)) that satisfies the assumption of hydrostatic equilibrium over a tight range of lunar CMB radii (. CMB = 381 +/- 12 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 within (367 +/- 100) years.

Plain Language Summary The study of the rotation of a body gives access to key information about its interior. Using a set of numerically integrated equations, Earth-Moon distance information from lunar laser ranging (LLR) data, and the knowledge of Moon's gravity from the Gravity Recovery and Interior Laboratory mission, we are able to simulate the rotation and motion of the Moon in the vicinity of Earth, Sun, and other planetary bodies with high accuracy. In this study, we compare the expected relaxed shape of the Moon's core with that obtained from a best-fit adjustment of our simulation parameters to the observed LLR data. This novel approach allows us to improve the previous uncertainty in the radius and polar flattening of the Moon's core-mantle boundary (CMB), both by a factor of 3. Limits on the size of the lunar CMB provide significant constraints to important works such as the Earth-Moon formation (e.g., giant impact) hypotheses. In addition, a better constraint on the lunar CMB radii translates to an improvement on the precision tests of fundamental physics using LLR data. Furthermore, our methods can be applied to study the influence of the liquid core on the rotation of other planets, especially Mars, with the recent advent of the InSight mission.