Unlike modern astronomers, Ptolemy (c. AD 135) had the good fortune to access Babylonian observations without having to reconstitute the Babylonian calendar. Greeks had prolonged contact with the Ancient Near East, and the translation of foreign dates into a familiar calendar had been taken care of by Ptolemy's predecessors.
Ptolemy's astronomical work, the Almagest, is based on the Egyptian calendar made up of 12 months of 30 days plus 5 extra days. The year has exactly 365 days, which eliminates the hassle of sorting out leap years and leap months when totaling the number of days between astronomical events.
The astronomical observations recorded in the Diaries provide strong support for conventional chronology, but their scope is limited. Of the 180 Diaries preserved and dated, only six tablets record observations prior to 400 BC - four from the 5th century and one each from the 6th and 7th.
The 6th century tablet, Diary No.-567, records more than 40 observations that were shown in Feat of Clay to corroborate the date -567. (See Caeno homepage)
A similar study can be carried out on the oldest Diary, No.-651. A transliteration of the cuneiform text along with an English translation is provided for hardy souls who wish to evaluate the evidence.
The Almagest logs nearly one hundred observations to which a precise date can be ascribed. The most ancient observations are from Babylon - three eclipses of the moon in the years 721 BC and 720 BC.
Although Ptolemy possessed Babylonian observations of older eclipses, he notes the triplet of 721/20 was the oldest recorded in an unambiguous way. Moreover, they conform to calculations based on an eclipse triplet that Ptolemy had personally observed.
One Babylonian eclipse quoted in the Almagest is also known directly from a cuneiform tablet. The date inscribed on the tablet is Cambyses Year VII Month IV (Duzu), night of the 14th; the Almagest writes 7th year of Kambyses, which is the 225th year from Nabonassar, Phamenoth 17/18.Modern computation agrees with the Cambyses tablet and the Almagest about the date of the eclipse, -522 July 17, but not much else. The three descriptions of the eclipse - Ptolemy's report in the Almagest, the account inscribed on the tablet and the computed one - do not match.
Lunar eclipses were the only Babylonian observations that entered Ptolemy's calculations. He judged their regular observations unreliable and argued convincingly for excluding them. Nevertheless, modern investigators find the Babylonians accurately observed and recorded many celestial events.
Presumably Ptolemy was aware that his calculations were incompatible with Babylonian observations, and he reacted as theorists often do - he focused on compliant evidence. Experimental results in complex studies are often contradictory. Hence the incongruous Babylonian data did not deter Ptolemy from the belief that celestial bodies move in perfect circles and have done so since time immemorial.