Hipparchic cycle

There are additional subtle and some imperfectly understood rates of change in both the lunar and solar cycles.

An eclipse cycle constructed by Hipparchus is described in Ptolemy's Almagest IV.2: For from the observations he set out he [Hipparchus] shows that the smallest constant interval defining an ecliptic period in which the number of months and the amount of [lunar] motion is always the same, is 126007 days plus 1 equinoctial hour.

This period is a multiple of a Babylonians unit of time equal to one eighteenth of a minute (⁠3+1/3⁠ seconds), which in sexagesimal is 0;0,0,8,20 days.

(The true length of the month, 29.53058885 days, comes to 29;31,50,7,12 in sexagesimal, so the Babylonian value was correct to the nearest ⁠3+1/3⁠-second unit.)

By comparing his own eclipse observations with Babylonian records from 345 years earlier, he could verify the accuracy of the various periods that the Chaldean astronomers used.

[citation needed] The Hipparchic eclipse cycle is made up of 25 inex minus 21 saros periods.

[3] It corresponds to: There are other eclipse intervals that also have the properties desired by Hipparchus, for example an interval of 81.2 years (four of the 251-month cycles, or 19 inex minus 26 saros) which is even closer to a whole number of anomalistic months (1076.00056), and almost equally close to a half-integer number of draconic months (1089.5366).

An exceptionally accurate eclipse cycle from this point of view is one of 1154.5 years (43 inex minus 5 saros), which is much closer to a whole number of anomalistic months (15303.00005) than the interval of Hipparchus.