Abstract
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.
Highlights
The gravitational attraction of the Moon at the Earth causes a tidal distortion of the oceans and solid Earth
Lunar tidal acceleration and recession rate The transfer of energy and angular momentum from the rotation of the Earth to the orbit of the Moon causes the length of day, the lunar distance, and the lunar orbit period to increase
The deceleration and other variations in Earth rotation needed to be determined with respect to a uniform physical time scale in order to determine the lunar tidal acceleration with respect to that time scale
Summary
The “Calculation of lunar orbit anomaly” paper by Riofrio [1] claims that the present 38.1 mm/yr Lunar Laser Ranging (LLR) value for the tidal recession of the Moon is 9–10 mm/yr too large because a decreasing speed of light causes an apparent increase in distance. To support this idea, evidence from geology, Earth rotation, and ocean model calculations are cited. Both lunar tidal recession rate and increasing orbit period (0.352 ms/yr), and compare the recent values with older determinations. Analysis of LLR data tests whether the speed of light is constant
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