Mean and true Sun

Question

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.

Answer 1

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:

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

Source:

• Historical Astronomy: Ancient Greeks: Hipparchus