Lunar Laser Ranging and the Drift of the Gravitational Constant in an Expanding Frame

Lunar laser ranging measures the Earth-Moon distance to centimetre precision and, through the orbital dynamics, limits any present drift of Newton's constant to 2.20e-12 per year at two standard deviations (Williams, Turyshev and Boggs). If the gravitational constant followed a power of the scale factor, the permitted power would be 3.07e-02. Extending that same power to nucleosynthesis would change the gravitational constant there by a factor whose fractional shift is 0.64 - far beyond what the light-element abundances allow - which shows that a pure power law cannot connect the two epochs and any real variation must saturate or switch off. Across the 4.5 billion year dynamical history of the Earth-Moon system the linear accumulation is at most 9.90e-03. Computed from published inputs, not measured.