New Formulas for Day Length, Solar Days per Year, and Lunar Distance in the Evolving Earth–Moon System

The Earth–Moon system has undergone continuous evolution across all timescales since its formation. Earth's rotation is gradually slowing, the Moon's rotation is decelerating, and the Moon is slowly receding from Earth. These progressive changes affect key planetary parameters, including the length of day (LOD), the number of days per year (DOY), and the Earth–Moon distance (DOM). Building on the author's earlier work, this paper presents a set of mathematical equations to model these dynamics and predict LOD, DOY, and DOM over time. The results derived from this model show strong agreement with historical data, offering a robust framework for understanding the long-term evolution of the Earth–Moon system. To address the longstanding Lunar crisis—where conventional tidal friction models predict an unrealistically close Earth–Moon proximity in the distant past and many assumptions and parameters must be introduced to help reconcile the models with observations—this study proposes a novel hypothesis: a significantly lower volume of surface liquid water in Earth's early history may have reduced tidal dissipation. The subsequent increase in oceanic volume could be attributed to the capture of a large icy comet, a scenario supported by precedent such as the 1994 collision of Comet Shoemaker–Levy 9 with Jupiter. This mechanism offers a plausible resolution to the tidal friction discrepancy and deepens our understanding of planetary evolution.