I recently learned about the Ptolemaic system, which seems pretty accurate. There is even a simulator on the Internet: https://astro.unl.edu/naap/ssm/animations/ptolemaic.html

You can see that there are parameters which are used to describe the planets motion and my question is simple:

Given the observations of the sky, how did Ptolemy (and the physicists that came after) adjusted these parameters so that the theory fits the observations ? Is there a method or is it purely by trials and errors?

Maybe the answer is simple but I'm not a physicist (though mathematically trained) and I was never taught Ptolemaic science!

  • $\begingroup$ I know how I would adjust the parameters today (non-linear optimization of the parameters of the model to fit observations), but I do not know the methods used in antiquity. In fact, that might be a better question for history of physics SE than this SE. $\endgroup$ – Anders Sandberg Jul 22 '19 at 9:44
  • $\begingroup$ @AndersSandberg : you are probably right. I taught it was the right place because I want the method used, not an historical investigation. $\endgroup$ – J.Mayol Jul 23 '19 at 9:09

One way in which Ptolemy adjusted his theory to fit observations was to create epicycles (small loops added to the orbit) to explain the apparent retrograde motion of Mars at a certain point of its orbit around the Earth, as was believed in those days. The real explanation was, of course, the fact that our speedier Earth overtakes Mars so that it appears for a short while that Mars is moving backwards. I sometimes wonder if modern physics has an equivalent of epicycles somewhere, and suggest that quantum mechanics is the best place to look for it.

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  • $\begingroup$ Epicycles can be viewed as adding extra Fourier components to a series. In a sense a lot of theories with somewhat arbitrary higher order corrections are epicyclical. Whether that is a sign that they could be replaced with a correct "heliocentric" theory explaining things better, or just that the underlying reality is a mess and best described by successive approximations, that is going to be domain-dependent. $\endgroup$ – Anders Sandberg Jul 22 '19 at 9:40
  • $\begingroup$ I have used an online planetarium which used Newtonian mechanics, but when a geocentric system was chosen the epicycles were there in all their glory. IMO it was a model that fit the data with many parameters, which is what makes newtonian gravity a better theory that fits the same data and predicts many more. $\endgroup$ – anna v Jul 22 '19 at 14:35
  • $\begingroup$ @Michael Walsby : this does not answer my question. I already knew the basic idea of the theory. The content of my question is how did Ptolemy adjusted the parameters (radius of the principal circle, excentricity, radius of the minor circle, apogee angle). $\endgroup$ – J.Mayol Jul 23 '19 at 9:06
  • $\begingroup$ @annav : I've seen that too, but I'm not asking why Newtonian gravity is a better theory or so ... $\endgroup$ – J.Mayol Jul 23 '19 at 9:07
  • $\begingroup$ You are asking how they measured? That is history of science. en.wikipedia.org/wiki/Astrolabe , wells at midday etc $\endgroup$ – anna v Jul 23 '19 at 9:20

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