The problem with the Ptolemaic system

Other than it’s wrong of course :wink:

I’m re-reading “A Brief History Of Time”, or rather the updated version “A Briefer History Of Time” as I have nothing better to read at the moment and It’s been about 10 years since I read the original so it’s about time.

In the beginning of the book Hawkins paints the modern picture of our universe by describing our past attempts at modeling it. The first two names that get mentioned are Aristotle and Ptolemy and specifically, the Ptolemaic system of the universe as one of our first models that (for the most part) fit human observation of the heavens.

So, I believe I understand the system as portrayed by Ptolemy. In the center is the Earth and the moon, sun, planets and stars all orbit the earth in “spheres”, each of those heavenly bodies also followed circular paths within their own “sphere” in what were called epicenters. These little circles essentially portrayed the planets as if they were themselves orbiting an unseen mass at the center of their own little orbits.

I understand why this had to be done for the planets. Since they too orbit the sun, just as the earth, their motion across the sky could not be explained as the fixed “sphere” of background stars could: with just a plain rotating sphere above earth. The planets literally seem to wonder about the sky as they follow their orbits around the sun.

In the book, however, Hawkins points out that Ptolemy understood that there was a problem with his system. Namely, that the moon, following it’s own epicenter, would need to sometimes be about 1/2 as close to the earth as it would at other times. But we would then expect the moon to appear twice as large in the night sky from time to time - something that obviously doesn’t happen.

And this is when I get lost. I understand why the epicenters would be needed to explain the seemingly odd motion of the planets in the sky… but the moon actually DOES orbit the earth. Why would epicenters be needed to explain it’s motion?? And the same goes for the sun as well, IMHO.

Where am I going wrong?

In that the Moon’s orbit is not circular.

There were two big steps in moving away from the Ptolemaic system:

  1. move the Sun to the center,
  2. get rid of the idea that the orbits Must Be Circles because Circles Are The Perfect Form.

Copernicus gets credit for the first one (1), Kepler for the second.
1: although he didn’t dare explain in life that this was how he was working, and his documents indicate that he thought of it as “a change in the frame of reference which makes the work simpler, faster and more accurate” and not necessarily closer to the truth than the more-complicated method

Ahhh, ok, so it’s the elliptical orbit of the Moon that required an epicenter to accurately predict it’s movement across the sky!

Makes sense. Thanks!

I admit it - I’ve not read A Short History of Time (Gasp!) but if this is what Hawkins is saying I think he is just wrong about the Ptolemaic system. As you point out, the moon does not need an epicycle(s). Epicycles are needed to explain the retrograde motion planets sometimes show - the moon just goes round the earth and does not exhibit retrograde motion against the fixed stars. The actual orbit is, as noted, an ellipse but it is not that eccentric.

See this sitefor a good explanation of Ptolemy’s system.


His name is Hawking, the book is A Brief History of Time, and the Almagest did indeed feature an epicycle for the Moon, as has already been explained in detail in Post#2. Other than that, there’s nothing wrong with your post.

It’s not grossly off, but it’s far enough off that a careful observer, even in pre-telescope times, could note the discrepancy.