The Equant point

Ptolemy was wrong. The Sun does not go round the Earth. Why did his view dominate our understanding for over 1300 years? Why was it so hard to change our minds?

Through the mediaeval period, Ptolemy superseded Aristotle’s understanding of celestial motion because he was more accurate. His theory could be used to predict where a planet would appear at future times. He was not only wrong about the Sun going round the Earth, but also about the celestial spheres: the planets were fixed to spheres, made of the etherial fifth element quintessence, and nesting within each other, else, how would they not fall to Earth? He was also wrong in holding to an Aristotelian idea, that because the Heavens are perfect, the planets must move in circles, because the circle is perfect.

The planets do not appear to move in perfect circles. They speed up and slow down, which is not perfect. Ptolemy’s answer was the Equant point. The Earth was not thought to be at the centre of the sphere on which the planet moved, but off-set. The equant point was also not at the centre: it was that place from which the planet would appear to move at a constant rate in its circle.

Ptolemy was right that Mars was closest to Earth, then Jupiter, then Saturn, because he decided that the slower moving planets were further away: but he had no reason for deciding that order.

He was a practical scientist, making new instruments for measuring the precise position of the planets more accurately than before. He was a mathematician, devising the mathematical models which enabled astronomers for centuries after to predict where the planets would appear.

Why would astronomers follow this false scheme? Because predicting the courses of the planets was a complex task. The student would learn the accumulated knowledge of humanity in making those predictions, the practical skills of observing and the mathematics, and so would have Ptolemy’s views inculcated. It was how it was. The observations slowly became more accurate with better instruments, diverging from Ptolemy’s mathematics; and it was important to measure the Heavens, because Easter fell on the first Sunday after the first full moon after the vernal Equinox: we must therefore know when the Equinox is.

Copernicus placed the Sun at the centre, but retained the Greek idea that orbits were circular. Tycho Brahe had the Sun moving round the Earth, but Mercury and Venus moving round the Sun: the spheres, then, could not be, as they would be moving through each other. Johannes Kepler theorised that the planets moved in ellipses rather than circles, and Newton calculated how gravity affected their movement. But Mercury does not fit Newton’s laws, and this could be observed by the 19th century: it was theorised that there was another planet, Vulcan, within the orbit of Mercury whose gravity influenced it. Einstein’s theory explained the orbit of Mercury without need for another planet.

Ptolemy and the muse Astronomia

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