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The Gravity Recovery and Interior Laboratory (GRAIL) mission has sampled lunar gravity with unprecedented accuracy and resolution. The lunar GM, the product of the gravitational constant G and the massM, is very well determined. However, uncertainties in the mass and mean density, 3345.56±0.40 kg/m3, are limited by the accuracy of G. Values of the spherical harmonic degree-2 gravity coefficients J2 and C22, as well as the Love number k2 describing lunar degree-2 elastic response to tidal forces, come from two independent
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Williams et al. (2014) studied this question.
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