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I studied the Farnese Atlas and I wonder how did the Ancients discover the ecliptic, the equator, etc. with the Ptolemaic system namely without knowing that the Earth rotates on itself, especially for the Ecleptic.

I ask the question because if in their model the Earth does not rotate, so how do they explain the two revolutions of the sun around the earth:

  • The first one being the daily cycle (sunrise and sunset)
  • The second one being the tropical year

With a model where the Earth does not rotate, I do not understand how they found out that the Sun make a revolution of a one year around the Earth (whence the ecliptic) with a second daily revolution. How could they conjugate these two Sun's cycles?

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  • $\begingroup$ They believed the whole celestial sphere rotated daily. $\endgroup$ – adrianmcmenamin Jul 2 '17 at 19:36
  • $\begingroup$ In that case how to explain they found out the ecleptic and the precession of the equinoxes? $\endgroup$ – moth Jul 2 '17 at 19:48
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The ecliptic was understood to be the path of the sun relative to the sky.

Ptolemy believed the sky rotated daily around the Earth. All the planets, including the Moon and the Sun, shared in this motion.

However, the planets had secondary motions, relative to the sky. And in particular relative to the stars that they thought were fixed to the sky. This motion was discovered by careful observations of the sky, and was very well known, long before Ptolemy.

The motion of the stars was very simple: therefore when Ptolemy was describing his system, he only concerned himself with the motion of the planets (including the moon and sun) relative to the stars. It was clear that the planets all approximately followed a great circle relative to the stars. This great circle is the ecliptic. The Sun's motion was the simplest. It was exactly on the great circle, and it's position relative to the stars moved almost evenly. The other planets (including the moon) had orbits that were less even, but by introducing a system of Eccentrics, Deferents, Epicycles and Equants, Ptolemy was able to account for nearly all their motions.

The precession of the equinoxes was noticed because the Greeks used a calendar based on the heliacal rising (the date that stars are just visible before sunrise) of certain stars. And it was noticed that the heliacal rising was changing relative to the seasons and the equinox. We understand the reason for this to be the precession of the equinoxes.

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I don't think the question was clearly phrased.

The question that I will answer is how did the ancients see the invisible line known as the ecliptic. The problem is similar in that it is easy to tell how far north and south you are but difficult to tell how far east and west you are.

You can just keep track of where the heart of the sun rises on the horizon and then match that point up with an equivalent point on the celestial sphere. You have to have a fairly good map of the heavens either drawn in your head or on paper. It would be easy to tell where the sun is North vs South but a little bit more difficult to see exactly where it is east to west. My guess is that they understood that the sun moves very steadily and they figured out its daily rate forward. This would have been confirmed during total eclipses hence the name ecliptic.

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They saw the stars, planets, Moon and the sun (the Celestial Sphere) rotate around the Earth each day. The Sun however, moved about 1 degree each day across the Celestial Sphere, so by the end of a year it moved 360 degrees. They called one full cycle of the Sun moving across the Celestial Sphere, a year. The planets (the word meant wanderers) moved each at slightly different and variable rates. The Sun, planets and the Moon moved along on roughly the same great circle on the Celestial Sphere. Since they traveled along the same path but at different rates, they would eclipse each other every so often. I guess that is why they called that great circle the ecliptic.

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This article describes it. https://www.ias.ac.in/article/fulltext/reso/011/03/0051-0068 Aryabhata described it and the Greeks most likely had a similar method. The title of this article is Aryabhata and Axial Rotation of Earth - Khagola (The Celestial Sphere)" by Amartya Kumar Dutta. There are a lot of diagrams here.

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  • $\begingroup$ Dutta's article does not appear to discuss the Ptolemaic system. $\endgroup$ – Mike G May 3 '19 at 11:48
  • $\begingroup$ I agree. It is sun centered. But the concepts of celestial sphere etc are similar. $\endgroup$ – Partha Shakkottai May 3 '19 at 17:01

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