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I have problems to understand the point of "mean sun" and "true sun". As I understood the mean sun is set in the center of the earth orbit (which is a circle). So Ptolemy, Copernicus and Brahe used the "mean sun", however they knew that this isn't the real position of the sun? Did they do that due to the reason it would fit with the mars oppositions?*

(*Three of them used circles to describe orbits of planets. But if they want to link that together with the observations it wouldn't fit.)

Is that right? So even Ptolemy knew that the sun isn't in the middle of the orbit of the earth?

Here is a website which I think describes it: http://science.larouchepac.com/kepler/newastronomy/part1/5/index.html http://science.larouchepac.com/kepler/newastronomy/part1/6/index.html

Due to my first language is not English it might be possible that I didn't understand some important aspects of the given links.

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    $\begingroup$ Ptolemy's conception was structurally geocentric, not heliocentric. In its final incarnation, I think Ptolemy had the Sun moving in a circular orbit with its center displaced from the Earth, and its angular velocity constant as seen from the equant (a point on the other side of the center of the Sun's orbit, such that it and the Earth were equally distant from that center). This sounds bizarre but it's a very close analogue to Kepler's first two laws, and was observationally indistinguishable from it until the invention of the telescope (no matter what Kepler might have written). $\endgroup$ – Brian Tung Apr 25 '17 at 22:57
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Yes, Ptolemy adopted Hipparchus's idea that epicycles and eccentric orbits could explain the irregular motion of the Sun. From David McClung's biography of Hipparchus:

Hipparchus also created the first reasonably accurate model of the motion of the sun and moon. Using the idea of epicycles, probably introduced by the mathematician Apollonius of Perga, he was able to create a model that accurately predicted some key positions of the moon's motion. He created a similar model to predict the position of the sun. (See the Ptolemy page for more information on epicycles and its subsequent use in the planetary models.) His model didn't work for all cases, but it marked the real beginning of trying to create a predictive model that matched data.

Even though the orbits are circular and going around the earth, the earth is not at the exact center of the orbits of the sun and moon. (They were eccentric orbits.) Hipparchus needed to use the epicycles and eccentric orbits because the observed motion of the sun around the ecliptic was not at a constant rate - in the winter the sun moved a little bit faster and in the summer the sun moved a little bit slower. Using an eccentric orbit for the sun and moon, and using small epicycles, Hipparchus gives the foundations of the classic Greek model of the solar system that approximately predicts the positions of the moon and sun that matched positions and predicted key dates and events pretty well. Eventually, Ptolemy takes this Hipparchan model and fully applies it to the motion of the planets - and eventually produces a full, working model of the solar system.

emphasis added

An epicycle is like an orbit along an orbit:

Epicycle

An eccentric orbit is an orbit where the inner body does not occupy the center point of the outer body's orbit.

Source:

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  • $\begingroup$ Today the explanation for irregular motion of the Sun is the elliptical orbit isn't it? At this time they didn't know that. So Ptolemy put the Earth not exactly in the middle of the circle. Like here: science.larouchepac.com/kepler/newastronomy/part1/exag.html And when Copernicus came, he just replaced the earth with the sun and also used the same position right? $\endgroup$ – Keplr Mar 24 '17 at 11:01
  • $\begingroup$ @Keplr Yes, that is part of it, but what that page leaves out is the epicycles. $\endgroup$ – called2voyage Mar 24 '17 at 22:44

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