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What are epicycles, deferents, eccentrics, equants, etc.? Who first introduced them, and when? Why were they introduced? How do they work? Are there visualizations of this?


e.g., what is St. Thomas Aquinas describing here in his commentary on Aristotle's De Cœlo (lib. 2 l. 17)?
To each of these he [Eudoxus or Aristotle?] assigned four movements, according to the four spheres that revolved the stellar body fixed in the lowest of them. Thus the first sphere moves the stellar body from east to west according to the diurnal motion; the second moves the stellar body in the opposite direction of west to east in the Zodiac — and this is called longitudinal motion; the third sphere moves a stellar body latitudinally, according to which a star is now in a more southerly, now a more northerly, position in the Zodiac. Now he placed the poles of this third sphere in the Zodiac; hence it followed that a major circle, equidistant from the poles, would go through the poles of the Zodiac. From this it seemed to follow that the planets in their latitudinal motion would sometimes reach the very poles of the Zodiac — a situation that never appears. Hence, he posited a fourth sphere that would move a star in an opposite direction to this movement and thus prevent it from ever reaching the poles of the Zodiac. He did not, however, attribute the motion of this fourth sphere to the sun and the moon, but tried to save their appearances by positing only three spheres, proportional to the first three of the other planets, but in such a way that the latitudinal motion of the moon would be greater than the sun's, as is explained in Metaphysics XII.

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All these words are from astronomy, used to describe the motion of the Sun, Moon and planets. The simplest model is this. Suppose that Earth is the center of a circle. This circle is called deferent. A point moves on the deferent with constant angular velocity, this point is called the center of the epicycle, and epycycle itself is a circle centered at this point. The planet moves on the epicycle with constant angular speed. In another equivalent model, earth is not in the center. But the center of the deferent moves on another circle which is called the eccenter. In more comlicated models the motion of the center of the epicycle is not uniform with respect to the center of the epicycle but uniform as seen from another point which is called equant.

I hope I explained all words. The two simplest models that I described in the beginning were introduced by Apollonius of Perga (262–190 bc) and he proved that they are equivalent. (In modern language this is equivalent to commutativity of addition of vectors). Hipparchus built first models for Sun and Moon, and possibly of planets using this machinery. Equant was introduced by Ptolemy (100-170 ad) who built a satisfactory model for the whole Solar system. This model, with minor variations was used successfully until 17th century, when it was replaces by Kepler's laws, where the motion is on ellipses and the angular velocity is not constant.

However the model with circles and uniform motion is a very good approximation that worked.

For more detail, see Ptolemy's Almagest.

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