$\Delta T$ and the Tidal Acceleration of the Lunar Motion from Eclipses Observed at Plural Sites

Abstract

An eclipse on 188 BC July 17 was observed and recorded both at Chang’an (China) and Rome (Italy). An eclipse on AD 873 July 28 was observed and recorded both at Nishapur (Iran) and Kyoto (Japan). The eclipse was annular at Nishapur. These plural records of deep eclipses are rare in history, and are useful for determining the clock correction, $\Delta T$, and the lunar tidal acceleration, $\dot{n}$. We have tried to determine as precisely as possible the ranges of these two parameters. If we fix the tidal acceleration to $- {25\rlap {.}{}^{\mathrm {\prime \prime }}83} \,\mathrm{cy}^{-2}$, we get, as a best estimate, $12581 \,\mathrm{s} < \Delta T < 12741 \,\mathrm{s}$ from the 188 BC eclipse and contemporary eclipses, and $3327 \,\mathrm{s} < \Delta T < 3498 \,\mathrm{s}$ from the AD 873 eclipse and contemporary eclipses.