Editing Hipparchus (section)

===Motion of the Moon===
{{further|Lunar theory|Orbit of the Moon}}

Hipparchus also studied the motion of the [[Moon]] and confirmed the accurate values for two periods of its motion that Chaldean astronomers are widely presumed to have possessed before him. The traditional value (from Babylonian System B) for the mean [[synodic month]] is 29&nbsp;days; 31,50,8,20 (sexagesimal) = 29.5305941... days. Expressed as 29&nbsp;days + 12&nbsp;hours + {{sfrac|793|1080}}&nbsp;hours this value has been used later in the [[Hebrew calendar]]. The Chaldeans also knew that 251 [[synodic month]]s ≈ 269 [[anomalistic month]]s. Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and is also close to an integer number of years (4,267 moons : 4,573 anomalistic periods : 4,630.53 nodal periods : 4,611.98 lunar orbits : 344.996 years : 344.982 solar orbits : 126,007.003 days : 126,351.985 rotations).{{efn|These figures use modern [[dynamical time]], not the solar time of Hipparchus's era. E.g., the true 4267-month interval was nearer 126,007 days plus a little over half an hour.}} What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within a tight range of only approximately ±{{frac|1|2}} hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million.

Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141&nbsp;BC and 26 November 139&nbsp;BC according to Toomer{{r|toomer1980}}) with eclipses from Babylonian records 345 years earlier (''Almagest'' IV.2{{sfn |Jones |2001}}). 

Later [[al-Biruni]] (''Qanun'' VII.2.II) and [[Nicolaus Copernicus|Copernicus]] (''de revolutionibus'' IV.4) noted that the period of 4,267 moons is approximately five minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no fewer than eight minutes.{{r|sf1993}}{{r|ssm1997}} Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. From modern ephemerides{{r|ccf2002}} and taking account of the change in the length of the day (see [[ΔT (timekeeping)|ΔT]]) we
{{Who|date=September 2024}} estimate that the error in the assumed length of the synodic month was less than 0.2 second in the fourth century&nbsp;BC and less than 0.1 second in Hipparchus's time.