"In order to correctly predict this position (of the celestial bodies), Ptolemy had to assume that the moon followed a path that sometimes brought it twice closer to the earth than at other times" (A brief history of time - Stephen Hawking).

I do not understand this: both in the geocentric as well as the heliocentric model, the moon just revolves around the earth... Why then should there be a correction for the moon? Who can help me with this? I searched on wikipedia and google but didn't found an answer.


1 Answer 1


The moon doesn't just "go round the Earth", at least not if you are attempting an accurate theory of the lunar motion. The moon appears to be moving faster at some times than others, there are periodic wobbles, and the plane in which the moon orbits changes relative to the stars.

The measurements of the position of the moon were really quite accurate by this time, and a theory that was a couple of degrees out was not acceptable to Ptolemy.

For various reasons, Ptolemy desired to use an epicyclic model. This model allowed him the flexibility to describe a wide range of motions. Ptolemy had inherited a model of the moon's motion from Hipparchus. This had a single epicycle and was quite accurate near full moon and new moon, but not sufficiently accurate at half moon. This is due to a motion of the moon now called "evection" We now describe evection as a distortion of the moon's elliptical orbit by the sun's gravity. Ptolemy described it as an epicyclic motion, which moved the centre of the Hipparchus's epicycle away from the main orbital circle in a monthly motion.

When all these motions are combined, the motion of the moon in the sky is excellently described by Ptolemy's theory. Indeed it describes the motion of the moon far better than a naïve application of Keplerian ellipses. But it does have the effect of quite significant variation in the distance of the moon from the Earth.

A neat summary of this can be found in Dr Robert Hatch's *Summary of Ptolemaic Astronomy

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A diagram showing Ptolemy's lunar theory.


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