# Earth's and Sun's rotation in the Ptolemaic world

In Ptolemy's geocentric model the Sun travels through the ecliptic and around the Earth once every 24 hours and the Earth does not rotate about its axis. What is Ptolemy referring to when he talks about the Sun's position during the year? How did he reconcile the Sun's eccentric orbit (giving rise to different length seasons) with the fact that the Sun rotated around the Earth every 24hrs?

• The fixed stars also rotate every 24hrs, the Sun's position is taken relative to them. What he describes is an approximation of the same trajectories we would come up with today in the frame attached to rotating Earth. What is there to reconcile? Commented Feb 26 at 10:44
• When, during the day, is the position of the Sun taken relative to the stars? At noon? From which part of the Earth? The position of the Sun (taken as a straight line between the Earth, the Sun and the point in the ecliptic this line points to) makes sense in a heliocentric model where the Earth moves by <1° per day, but makes less sense in a geocentric model where the Sun moves 360° per day (180° during daytime). Commented Feb 26 at 10:52
• Seasons don't make sense in a model where Earth's inclination is fixed relative to the Sun Commented Feb 26 at 10:54
• Ancient Greeks did not explain seasons as we do today, they had stories about Hades and Persephone. But since the two models are geometrically equivalent whatever makes sense in one makes it in the other. If you want to explain seasons by the tilt that tilt will just be reflected geocentrically in the position of the ecliptic, see How do geocentric theories explain seasons? on Physics SE. Commented Feb 26 at 12:19
• @Conifold good point Commented Feb 26 at 13:07

In Ptolemy system, there is a sphere of fixed stars which rotates about the Earth with constant speed 1 rotation per 24 hours. This rotation is about the axis which passes through the North and South pole. The poles are fixed with respect to the stars, and the great circle equidistant from the poles is the (celestial) equator. (Well, almost fixed, see below about precession).

All other motions in the sky are referred to this sphere of fixed stars. (So mathematically it is completely equivalent to diurnal rotation of the Earth).

Sun moves on the ecliptic, which is the great circle (fixed in the sphere of fixed stars) which is inclined to the equator. The period of this rotation is 1 year, and it is slightly non-uniform ("inequality of the Sun").

This theory gives a perfect account of the seasons which is essentially the same as our modern explanation. (Contrary to what @Conifold says in his comment). Ecliptic intersects the equator at two points which are called the Spring and Autumn equinoxes. In the middles of the corresponding arcs of the ecliptic there are two points at the greatest distance from equator. They are called the winter and summer solstices. The seasons are the intervals between these 4 points. It is an early discovery (before Hipparchus) that the seasons have unequal lengths. The conclusion is that the motion of the sun along the ecliptic is slightly non-uniform. This was called the Inequality of the Sun, and it corresponds in modern astronomy to the first and second Kepler's laws).

So it is hotter in summer, because a) the rays of the sun hit the Earth under bigger angle, and b) the days are longer).

In addition to this, the position of the equator (and thus of the poles) with respect to the stars and ecliptic is not exactly fixed; the points of equinoxes move with the period roughly 1 degree per century. This motion is called precession. (This is an ancient estimate, modern speed of precession is 1 deg per 71.6 years).

This is a more or less complete description of the Ptolemy's theory about Earth and Sun. Mathematically it is EQUIVALENT to the modern description. The difference between Ptolemy's and Kepler's description only concerns the motion of the Moon and planets.

Another difference, between the "Sun inequality" and the first two Kepler laws, is so small that it was undistinguishable for the accuracy of observations 18th century. For planets, Ptolemy theory also gives very good results. The inadequacy of his description was only detected in the end of 16th century as a result of improvement of observation accuracy (of Tycho Brahe). The most difficult case is that of the Moon. There was a continuous progress in describing the Moon motion since Ptolemy to the beginning of 20th century when a theory consistent with all observations was finally achieved.

• How come the Sun takes a year to go around the ecliptic and rises and sets every day (and hence must be going around the ecliptic every day)? What am I missing? Commented Feb 26 at 14:28
• You are missing the first paragraph of my answer. Ecliptic is fixed with respect to the stars. And the whole sphere of the fixed stars rotates with the speed 1 rotation per 24 hours. This motion accounts for daily rising and setting of the Sun (and of all fixed stars). Sun moves on the ecliptic (1 turn per year with respect to stars) and participates in the diurnal rotation of the whole together with all stars. Commented Feb 26 at 14:32
• If I'm understanding you correctly you are saying that the Sun moves along the ecliptic (and around the Earth) at a fixed speed of 24hrs per revolution. The sphere of the stars instead moves at a speed which is slightly faster than this so that we observe the progress in the night sky over the course of the year. This makes sense, but why does Ptolemy always talk about the Sun moving at the rate of one revolution around the ecliptic per year? Why doesn't he talk about the sphere of the stars moving instead? It would be way clearer in this case. Commented Feb 26 at 15:23
• Ptolemy uses the sphere of the stars as the reference. All motions that he discusses are WITH RESPECT TO THIS SPHERE. Except the rotation of the sphere itself around Earth with the speed 1 rotation in 24 hours. The reason for choosing this frame of reference is simplicity. Of course, it will be even simpler to consider the Earth rotating about its axis. But this Ptolemy rejects on the (wrong) physical reasons. Commented Feb 27 at 3:55