The story of our gaining an understanding of the planetary motions now begins. It allows us to examine how science works, in slow motion (about 15 centuries worth)  The heavens themselves, the planets, and this centre

Ptolemylived around 150 AD, and elaborated the geocentric (earthcentered) model of the solar system that prevailed until around 1500 AD. His model lasted for such a long time because it was able to match the existing observations of the positions of the planets reasonably well. (pictures from Bill Arnett, Graham Hart http://www.seds.org/billa/psc/theman.html) See http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Ptolemy.html, also http://www.hps.cam.ac.uk/starry/ptolastrol.html) Well do I know that I am
mortal, a creature of one day.  Ptolemy's epigram, from the Almagest, probably written by himself 
Key point: Development of a true scientific theory for the motions of the planets
He started with a large body of observations and a small number of "simple" assumptions for planet motions that had been proposed by earlier Greek astronomers (rejecting Aristotle's crystalline spheres).
His work is described in the "Almagest"  the Arabic title of the work, meaning roughly "Great Work." To fit the motions well, he had to use complex combinations of motions around circles that were moving on circles, and so forth. Working all of this out was a triumph of detailed mathematics. This illustration is from a translation of Ptolemy's Almagest from Arabic to Latin by Gerard of Cremona in 1175. The image shows the motion of the superior planets—Mars, Jupiter, and Saturn. (From Library of Congress Vatican Exhibit http://www.ibiblio.org/expo/vatican.exhibit/exhibit/dmathematics/Greek_math2.html) 
In this scheme, a retrograde episode looked like this (from Journey Through Astronomy, http://csep10.phys.utk.edu/): 
However, his accurate calculations demonstrated that the positions of the planets could only be explained if the circles at the basis of planetary motions were offset from the earth, so the constant motion was around a point in space rather than the earth. By precise adjustments of this nature, he was able to find a system that reproduced the planetary positions relatively accurately. Although we tend to present his model as simple sketches, his real work was a huge body of accurate calculations that allowed him to adjust the model to provide an accurate fit to the observations of the positions of the planets.
In common with another great astronomer, Kepler, Ptolemy also wrote on astrology
It had convincing strong points:
Thus, it was a good scientific theory for its time. With 20/20 hindsight, it had some weaknesses too:
Urania, Greek muse of astronomy, by Simon Vouet, http://www.luminarium.org/sevenlit/james/urania.htm 
Comet Halley in the Bayeux Tapestry 

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