The sources of error in historical dating are legion, but seldom is the date of a lunar eclipse in doubt. Nearly 2000 years ago Ptolemy was confident he could compute eclipse dates many centuries in the future (and the past.) However, determining the start of ancient eclipses, their duration and other characteristics presents a complex of issues not yet resolved.
One difficulty stems from the non-Newtonian forces acting in the solar system. Newton's equations cannot account for the effect of ocean tides on astronomical observations. The formulas specify that tides impede the rotation of the earth, but only experimental evidence can quantify the slowing down.
To an observer on earth, tidal friction slowing down the rotation of the earth is equivalent to a speeding up (acceleration) of the sun's progress in the course of a day.
The tidal action also affects the motion of the moon. According to Newton's 3rd Law, the moon experiences an equal and opposite reaction to the tidal force it exerts on the earth. The reactive force causes the moon to spiral away from the earth and slow down (negative acceleration). A precise determination of these accelerations is essential for calculating an accurate description of eclipses.
The effort to match modern calculations to ancient records reaches across time and space. A recent comprehensive study analyzes Babylonian, Chinese, ancient Greek and Arab timings of solar and lunar eclipses. Still, all too often the computed characteristics of an eclipse do not match the ancient report.
In addition to mathematical procedures, the dating of eclipses in Babylonian records requires a workable contemporary calendar.
The seminal work was completed half a century ago, and subsequent improvements have been rare. The study determined the placement of intercalary (leap) months in the Babylonian calendar, and then linked the first day of every month to a Julian calendar date.
As a bonus, the authors assembled the available evidence for the beginning of every reign from 626 BC to AD 75, in effect providing a Babylonian chronology of the period.