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According to Wikipedia, usage of the Sun's position as the basis for a celestial coordinate system dates back at least to Babylonian times, and the current "First Point of Aries" system dates back to 130BC.

My question is, how did they measure the position of the Sun with respect to other stars? By definition, any attempt to measure the Sun's position would be in the day time when no other stars were visible.

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The trick, as explained in the Almagest (which I have translated to French; see https://ecliptiqc.ca/Almagest.php) is to measure the Sun–Moon angular distance, then wait for it to be dark enough, then measure the angular distance of the Moon to some stars. By knowing the motion of the Moon for the time between the two observations, it is easy to reduce the observations and derive coordinates for the stars.

The Sun’s position was calculated more than measured. Knowing that the ecliptic crosses the celestial equator at the vernal point (aka “first point of Aries”) and at the autumnal equinox, and giving these points the longitudes 0° and 180°, respectively, you can derive the Sun’s ecliptic longitude on any day of the year.

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  • $\begingroup$ A very good French translation of the Almagest already exists, FYI (see here for volume 1), with detailed historical comments. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Jul 10, 2022 at 15:47
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    $\begingroup$ @Carl-FredrikNybergBrodda: I know of this translation, but it’s not “very good.” There are mistakes in it, both caused by Ptolemy (that other translators, such as Manitius or Toomer, have fixed) or caused by Halma. Also, French language has evolved quite a bit in the 200+ years since this translation. Plus, I’m making it partly interactive in a website, etc. (Plus, the most important: I’m having fun!) $\endgroup$
    – Pierre Paquette
    Commented Jul 11, 2022 at 0:14
  • $\begingroup$ Ah, I only had second-hand information that it is very good. Could you share some specific issues with it? Also: I certainly would never discourage a new translation of old work :-) $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Jul 11, 2022 at 0:25
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    $\begingroup$ Oh! it’s nothing major, but a few small things here and there… For example, in Book 4, the Greek version says “ὄγδοον” (eighth), but Halma translated by “un tiers” (one third). In Book 3, for a diagram, he extends the wrong line. And stuff like that, maybe three or four times in each Book (there are 13 books). Also, he didn’t verify Ptolemy’s calculations, so errors are propagated. I’m all for sticking to the original, but sometimes, emendation is a good thing. $\endgroup$
    – Pierre Paquette
    Commented Jul 11, 2022 at 0:53
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    $\begingroup$ As a follow-up… I’m in a section where Halma committed many transcription mistakes… I’ve counted 12 of them in Book 10, Chapters 1–7, and I’m not done translating Chapter 7 yet… Things like, for example, 4;25 in the French version while the Greek has δ̅ λεʹ (4;35). They abound. $\endgroup$
    – Pierre Paquette
    Commented Jul 19, 2022 at 3:20
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In the Last part of Astronomia Nova (Ch. 69) Kepler describes a way the ancient astronomers might did it. Kepler suspects this way Ptolemy was using but he is not sure. The process can be generally described as such:

  1. Using the Merdian altitudes one can infer where are the equinoxes (at least in time); (though Ptolemy might be using Alexandrian armillaries)

  2. Once The obliquity of Earth was known, one could use the declination (direct from observation of Merdian altitude) to know the elongation (ecliptic longitude distance) of the Sun from the equinox. this is done by simple spherical trigonometry calculation.

  3. One can during the day find the angular distance between the Sun and the Moon.

  4. then at night, we have the Moon and can see the distance of the Moon from the fixed stars that are visible at night - say star X.

  5. Now we basically have everything. we have the distance X-Moon; Moon-Sun; Sun-equinox. So we have the angular distance between X and the equinox.

It should be stressed that the ancients - up until the great Tycho Brahe -had severe issues in their Theory of Sun. Tycho got wrong the location of the Sun in about 7 minutes of arc at the equinoxes; this is mainly due to refraction and parallax issues which they knew existed but took the wrong quantities.

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