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!