Secular Recession of the Moon and Variation in Earth's Length of Day from Historical Lunar Eclipse Timings

The tidal interaction between the Earth and the Moon produces a long-term exchange of angular momentum that causes the Moon to recede from Earth while simultaneously increasing the length of day (LOD). This study applies a systematic analysis of three centuries of total lunar eclipse timing data drawn from the NASA Five Millennium Canon of Lunar Eclipses. By quantifying the variation in eclipse durations and computing observed minus calculated (O–C) differences, we infer secular changes in ∆T and consequently estimate both the lunar recession rate and the secular increase in Earth’s day length. Regression analysis of eclipse records indicates that the lunar recession rate is consistent with modern Lunar Laser Ranging (LLR) results within error margins, while long-term variations in LOD suggest complex tidal dissipation processes. The results demonstrate that eclipse records  provide a powerful natural chronometer for testing Earth-Moon dynamical models across historical timescales.