Glossary Y


Analemma fishburn
Superimposed images of the Sun taken through the
year at the same time of day yield a shape known
as an analemma. Image: Wikimedia Commons.
Year. Traditionally, the time taken for the Sun to return to the same position in the sky. In modern terms, the time taken for the Earth to complete one revolution of the Sun. Technically, this is known as the tropical year, from τροπικός 'pertaining to the solstice' since it marks the period in which the Sun travels from a given solstice to the same solstice. This period is 365.242188 days which implies a mean motion of 0° 59' 08.331'' (0.985647°) per day.
     Owing to the fact that the rotational axis of the Earth is inclined to the plane of its orbit (also known as the obliquity of the ecliptic) the progress of the Earth around the Sun gives rise to the phenomenon of the seasons, and it is the cycle of the seasons that underlies our fundamental notion of the year.
     The sun appears to rise in the east and set in the west but the exact path it takes in the sky day by day varies because the points on the horizon where it rises and sets differ each day until they repeat one year later. On any given day and time, therefore, the Sun will not be in the same position as it was yesterday or will be tomorrow, but a year later, at the same time of day, it will be.
      Even today, the tropical year is what most people mean by a year, but modern astronomy, and indeed modern society, has identified many other types of year:
  • anomalistic year;
  • calendar year;
  • Gregorian year;
  • Julian year;
  • sidereal year.
Determining the length of the year was a preoccupation of many ancient astronomers, prompted by their desire to produce a more accurate calendar. The C2nd CE Roman writer Censorinus, for example, lists (The Birthday Book 19) a few of what were probably a great many estimates made in antiquity:
  • Harpalos (early C5th BCE), 365 + 13/24 (365.5417) days;
  • Oinopides (early C5th BCE), 365 + 22/59 (365.3729) days;
  • Philolaus (mid C5th BCE), 364 + 1/2 (364.5000) days;
  • Meton (late C5th BCE), 365 + 5/19 (365.2632) days;
  • Kallippos (late C4th BCE), 365 (365) days;
  • Aristarchos (early C3rd BCE), 365 + 1/1623 (365.0006) days;
  • Aphrodisius (?), 365 + 1/8 (365.1250) days;
  • Ennius (early C2nd BCE), 366 (366.0000) days.
However, not all of these may be completely reliable reports since Censorinus was not primarily an astronomer but a grammarian. Indeed, we find that Hipparchos (C2nd BCE) in his book On Intercalary Months and Days, as reported by Ptolemy (Almagest 3.1; H207), mentions different values for both Meton (365 + 1/4 + 1/72 = 365.263889 days), and for Kallippos (365 + 1/4 = 365.25 days) to those quoted by Censoriuns. This latter figure of 365.25 days, which is overlong by 11 minutes and 15 seconds, soon became widely accepted as a good approximation. It was echoed by Geminos (Introduction to the Phenomena 1.7) in the C1st BCE and was subsequently made the basis of the Julian calendar developed by Sosigenes in 45 BCE. The current Gregorian year averages 365.2425 days which is just 27 seconds too long.
     Ptolemy, using his own observations of the autumn and spring equinoxes in conjunction with those of Hipparchos nearly three hundred years earlier, arrived at the following values (Almagest 3.1; H204): 365 + 1/4 − 1/20 (=365.2) days and 365 + 1/4 − 1/300 (=365.246667) days respectively. In addition, by comparing his observation of the solstice with those of Meton and Euktemon (Almagest 3.1; H206), he found a value of 365 + 1/4 − (23/24) × ( 1/571) (=365.248322) days. Similarly, he reports (Almagest 3.1; H207) that Hipparchos, using a summer solstice observation by Aristarchos in conjunction with his own, arrived at a figure of 365 + 1/4 − (12/24) × ( 1/145) (=365.246552) days, but sums up his survey by saying that Hipparchos later revised this figure slightly upwards in his book On the Length of the Year to  365 + 1/4 – 1/300 (=  365.246667) days. This figure exceeds the tropical year (365.242188 days) by 6 minutes and 27 seconds. Finally, Ptolemy himself agrees (Almagest 3.1; H208) with Hipparchos' revised value, restating it as 365 + 14/60 + 48/3600 (= 365.246667) days, concluding that this was the best approximation that could be had.
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