The past and present Earth-Moon system: the speed of light stays steady as tides evolve.

Tides induce a semimajor axis rate of +38.08 ± 0.19 mm/yr, corresponding to an acceleration of the Moon's orbital mean longitude of -25.82 ± 0.13 "/cent², as determined by the analysis of 43 yr of Lunar Laser Ranging (LLR) data. The LLR result is consistent with analyses made with different data spans, different analysis techniques, analysis of optical observations, and independent knowledge of tides. Plate motions change ocean shapes, and geological evidence and model calculations indicate lower rates of tidal evolution for extended past intervals. Earth rotation has long-term slowing due to tidal dissipation, but it also experiences variations for times up to about 10⁵ yr due to changes in the moment of inertia. An analysis of LLR data also tests for any rate of change in either the speed of light c or apparent mean distance. The result is (-2.8 ± 3.4)×10^-12 /yr for either scale rate or -(dc/dt)/c, or equivalently -1.0 ± 1.3 mm/yr for apparent distance rate. The lunar range does not reveal any change in the speed of light.