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).

• Planets move at uniform speeds
• Planets move on circular paths
• Planets move on a combination of circular paths including a small circle called an epicycle. This was required to explain the retrograde motion of a planet.

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/d-mathematics/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.

It had convincing strong points:

• It fit all of the available data.
• It predicted the earth was standing still, in agreement with observation (even though we now know that this observation was wrong).
• It predicted approximately where the planets were found even centuries after Ptolemy died.

Thus, it was a good scientific theory for its time. With 20/20 hindsight, it had some weaknesses too:

• Its predictions tended to drift relative to reality and needed to be adjusted from time to time using more observations.
• Was it the simplest possible model? (Modern scientists prefer theories with the fewest possible assumptions; this precept is called Occam's razor).
• It contained no underlying physical principles -- it was only geometry

Ptolemy's work was saved from being lost and forgotten because an Islamic center of intellectual inquiry developed in Bagdad, where scholars translated many of the Greek works into Arabic. Note that the drawing of the orbits of Mars, Jupiter, and Saturn reproduced above was translated from the Arabic, and thus was taken from the Islamic translation 1000 years after Ptolemy died. The Islamic scientists made a number of important contributions to our understanding as well as preserving older work. (from "Islam and the Arab World", Edited by Bernard Lewis American heritage Publishing Co., Inc. New York. P.200 http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.shtml )

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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