Hipparchus
Apparent motion of the Sun

Before Hipparchus, Meton, Euctemon, and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice) on 27 June 432 BC (proleptic Julian calendar). Aristarchus of Samos is said to have done so in 280 BC, and Hipparchus also had an observation by Archimedes. He observed the summer solstices in 146 and 135 BC both accurately to a few hours, but observations of the moment of equinox were simpler, and he made twenty during his lifetime. Ptolemy gives an extensive discussion of Hipparchus's work on the length of the year in the Almagest III.1, and quotes many observations that Hipparchus made or used, spanning 162–128 BC, including an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs by 5 hours from the observation made on Alexandria 's large public equatorial ring that same day (at 1 hour before noon). Ptolemy claims his solar observations were on a transit instrument set in the meridian.

At the end of his career, Hipparchus wrote a book entitled Peri eniausíou megéthous ("On the Length of the Year") regarding his results. The established value for the tropical year, introduced by Callippus in or before 330 BC was 365 + 1 ⁄ 4 days. Speculating a Babylonian origin for the Callippic year is difficult to defend, since Babylon did not observe solstices thus the only extant System B year length was based on Greek solstices (see below). Hipparchus's equinox observations gave varying results, but he points out (quoted in Almagest III.1(H195)) that the observation errors by him and his predecessors may have been as large as 1 ⁄ 4 day. He used old solstice observations and determined a difference of approximately one day in approximately 300 years. So he set the length of the tropical year to 365 + 1 ⁄ 4 − 1 ⁄ 300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the modern estimate of the value (including earth spin acceleration), in his time of approximately 365.2425 days, an error of approximately 6 min per year, an hour per decade, and ten hours per century.

Between the solstice observation of Meton and his own, there were 297 years spanning 108,478 days; this implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14 / 60 + 44 / 60 + 51 / 60), a year length found on one of the few Babylonian clay tablets which explicitly specifies the System B month. Whether Babylonians knew of Hipparchus's work or the other way around is debatable.

Hipparchus also gave the value for the sidereal year to be 365 + 1 / 4 + 1 / 144 days (= 365.25694... days = 365 days 6 hours 10 min). Another value for the sidereal year that is attributed to Hipparchus (by the physician Galen in the second century AD) is 365 + 1 / 4 + 1 / 288 days (= 365.25347... days = 365 days 6 hours 5 min), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1 / 4 + 1 / 144 days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear whether Hipparchus got the value from Babylonian astronomers or calculated by himself.
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