File:Length of Hipparchic period zoomed in.png

English: Lengths of the intervals between two solar eclipses separated by a Hipparchic period ending in 2001-2050. The red points are for intervals going from an eclipse at the descending node to an eclipse at the ascending node, and blue points are for intervals going from ascending to descending node. The groups of points linked by green lines represent groups in which the starting eclipses (and the ending eclipses) are separated by six months. The scale on the right is the number of hours when the interval is expressed as a number of days plus a number of hours. We see that the variation is quite small, because of the fact that the Hipparchic period is 4573.002 anomalistic months and 344.979 anomalistic years and these are close to whole numbers.

Both the red points and the blue points exhibit waves of period 18.6 years, peaking when the two eclipses are near the time when the earth is at aphelion (early July). There is theoretically another, smaller, component of period 6 years peaking when the two eclipses occur when the moon is near its apogee, but the amplitude is very small.

In the Almagest Ptolemy gives the length as 126007 days and one hour, but in fact the average is only 126007 days and half an hour.