Ptolemy: The Almagest

Ptolemy was an astronomer who lived in Alexandria, in Egypt, about 1,900 years ago. He wrote a giant book that explained how to predict where the Sun, the Moon and the planets would be in the sky, years ahead. People used it for about 1,400 years.

Ptolemy thought the Earth stood still in the middle, with everything else going around it. The tricky part was the planets. Mars, for example, usually drifts slowly eastward against the stars, night after night. But every two years or so it slows down, goes backward for a few weeks, then turns forward again!

Ptolemy explained this with a circle on a circle. Mars rides around a small circle, and the center of the small circle rides around a big circle. When Mars is on the inside of its small circle, it seems to go backward.

Who, when and why

Claudius Ptolemy (c. AD 100–c. 170) worked in Alexandria under Roman rule. His observations date from AD 127 to 141. He called his great work the Mathematical Composition; Arabic translators called it al-majisti, "the greatest", which became Almagest in Latin. He also wrote major books on geography, optics, music theory and astrology.

The problem he faced was prediction. Greek astronomers had believed for centuries that heavenly motions must be built from uniform circles. Hipparchus (c. 190–c. 120 BC) had made this work for the Sun and Moon, but his books are lost. Nobody had produced a full, working theory for the planets, with tables anyone could use to compute their positions. Ptolemy did.

What the Almagest contains

Circles on circles

For each planet Ptolemy used a big circle, the deferent, around the Earth, and a small circle, the epicycle, whose center rides along the deferent. The planet moves on the epicycle. When the planet is on the near side of its epicycle, moving opposite to the epicycle's center, it appears to move backward: retrograde motion.

Ptolemy added two refinements. The Earth is set a little off the center of the deferent (an eccentric). And the epicycle's center moves at a steady angular speed not as seen from the Earth or from the deferent's center but from a third point, the equant, placed on the other side of the center from the Earth. The equant broke the old rule of uniform motion about a circle's center, and many later astronomers disliked it, but it made the predictions much better.

Why he kept the Earth still

Ptolemy knew of the idea that the Earth turns. He rejected it with physical arguments: if the Earth spun, clouds and birds and things thrown upward would be left behind toward the west. Answering that objection needed a new physics of motion, which came with Galileo and Newton. Ptolemy was not being stubborn; with the physics of his day, a moving Earth looked impossible.

What later science kept, and what it changed

• Kept: the star magnitude scale (modern astronomers still use it, made precise in 1856); much of the trigonometry; the practice of building a model, comparing it with observations and adjusting it.
• Changed: the Earth moves (Copernicus, 1543); orbits are ellipses, not circles on circles (Kepler, 1609); all of it follows from gravity (Newton, 1687).
• An echo: Kepler's second law makes a planet sweep out equal areas in equal times. Seen from the empty focus of the ellipse, the planet then moves at a nearly steady angular rate, which is just what Ptolemy's equant did.

Saving the appearances

Did Ptolemy think his circles were real, or only a way to compute? He seems to have thought both mattered. In the Almagest he aims at models that predict; in a later work, the Planetary Hypotheses, he builds them into a physical system of nested shells and estimates the size of the universe. Medieval astronomers argued about whether astronomy describes the world or only "saves the appearances". The same argument came back when Copernicus's book was published with a preface (not by Copernicus) saying the Sun-centered system was only a calculating device.

Historians also debate how much of Ptolemy's star catalog came from Hipparchus, about 265 years earlier. Most think Ptolemy used and updated Hipparchus's work, as he says he did in places; a few have argued he copied more than he admits.

A long life

The Almagest was translated into Arabic in the 800s, and astronomers in Baghdad, Damascus, Maragha and Samarkand checked and improved it. Ibn al-Shatir in Damascus (1300s) replaced the equant with extra small circles in a way very like Copernicus's later models. Gerard of Cremona translated it from Arabic into Latin in 1175. Copernicus learned astronomy from it, and his own book follows its plan.

Big questions

• If a theory predicts well but is built on a wrong picture, is it a good theory?
• Ptolemy's model worked for 1,400 years. Why might people keep a model that works even when it seems strange?
• How would you convince someone that the Earth moves, using only what you can see from your backyard?