Editing Hipparchus (section)

===Apparent motion of the Sun===
{{More citations needed section|date=July 2024}}
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&nbsp;BC ([[proleptic Julian calendar]]). [[Aristarchus of Samos]] is said to have done so in 280&nbsp;BC, and Hipparchus also had an observation by [[Archimedes]]. He observed the summer solstices in 146 and 135&nbsp;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&nbsp;BC, including an equinox timing by Hipparchus (at 24 March 146&nbsp;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&nbsp;BC was {{frac|365|1|4}} days.{{r|leverington2003}} 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 {{frac|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 {{frac|365|1|4}} − {{frac|1|300}} days (= 365.24666... days = 365&nbsp;days 5&nbsp;hours 55&nbsp;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&nbsp;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&nbsp;days;14,44,51 (sexagesimal; = 365&nbsp;days + {{sfrac|14|60}} + {{sfrac|44|60{{sup|2}}}} + {{sfrac|51|60{{sup|3}}}}), 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 + {{sfrac|1|4}} + {{sfrac|1|144}} days (= 365.25694... days = 365&nbsp;days 6&nbsp;hours 10&nbsp;min). Another value for the sidereal year that is attributed to Hipparchus (by the physician [[Galen]] in the second century AD) is 365 + {{sfrac|1|4}} + {{sfrac|1|288}} days (= 365.25347... days = 365&nbsp;days 6&nbsp;hours 5&nbsp;min), but this may be a corruption of another value attributed to a Babylonian source: 365 + {{sfrac|1|4}} + {{sfrac|1|144}} days (= 365.25694... days = 365&nbsp;days 6&nbsp;hours 10&nbsp;min). It is not clear whether Hipparchus got the value from Babylonian astronomers or calculated by himself.{{sfn|Neugebauer|1975|loc=Vol. 1, pp. 293, 294}}