# Ptolemy was not so wrong ?

Hi all,
the Ptolemaic geocentric system was accepted for ~2000 years before Galilei discovered (by telescope) that Venus goes around the Sun, not the Earth.
However, AFAIK the Ptolemaic system reproduced the observations quite well (to a precision of 10' or so).
Let's not talk here about crystalline spheres and such. Let's just talk about the mathematical content. AFAIK, it can be shown that the Ptolemaic system (with epicycles) is roughly equivalent to the Keplerian system (if you use enough epicycles, neglect planet's brightnesses and any telescopic evidence, and, most important, use the right parameters).

After all, astrology has been done all thru the ancient times & middle ages, and astrological predictions (ephemerides) were correct to a certain degree, weren't they?

My question: Where can I find a mathematical representation of the Ptolemaic system, especially the exact values of all parameters used? Is there any tables/software/applets on the web, especially to show where it agrees/disagrees with the modern system?

Any help will be greatly appreciated.

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Ptolemaic accuracy was highest for the inner planets Mercury and Venus. But the theory had real problems with two important bodies.

1) The moon. The moon is affected by both the gravity of the sun and the earth. This gives it a complex motion which is tough to model in anybody's theory (Newton got it wrong!) Ptolemy's theory was bad in two ways, it wasn't accurate and it required big swings in the moon's distance from earth, which would have made big changes in its apparent size, which of course we don't see.

2) Mars. This is the biggy that inspired Copernicus and Kepler. The plane in which the orbit of Mars lies is tilted quite a bit with respect to the plane of the earth's orbit. This makes the "up and down" observed motion of Mars above and below the ecliptic an issue which Ptolemy couldn't solve. Copernicus showed the way by proving the centers of both orbits are in the sun. Then Tycho made super accurate observations of the oppositions of Mars to the sun, which gave Kepler the data he needed to develop his three laws.

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There are two modern translations of the Almagest. One of them is in the Great Books series, and I have it. It has sort of minimal editorial material. The other one I saw at our local library, and is a fine job. The scholarly apparatus is excellent. I don't know any modern edition of the Alfonsine tables, but you might look up Georg Purbach or Regiomontanus, renaissance table makers in the Ptolemaic tradition. There were a lot of Islamic table makers too.

The Almagest is a remarkable book. It tells you how to recreate astronomy in your own (presumably astronomically impoverished) part of the world. How to make the instruments, such as they were, how to do observations, even how to calculate your own trig tables (no sines, etc, they used chords, but they could solve spherical triangles so who cares?). And after turning you into an astronomer it offers you a part in an exciting cross-century program, to compute the precession of the equinoxes. And this self help book did in fact create astronomy in more than one civilization.

No wonder the Byzantines called it He Megiste, the greatest.