Caption: The Ptolemaic system (AKA the geocentric Ptolemaic solar system) illustrated by NAAP Applet: Ptolemaic System Simulator.

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Note the Ptolemaic System Simulator always puts the Sun's orbit outside of the planetary orbit.

This is WRONG for superior planets in the Ptolemaic system---it's not a bug, it's a feature.

Also you can override the actual type of a planet as a superior planet or an inferior planet with the superior planet or inferior planet type buttons.

1. The Ptolemaic system formulated by Ptolemy (c. 90--c. 168 CE) circa 150 CE is an epicycle model.

   The Ptolemaic system is fully explicated in Ptolemy's book the Almagest (as posterity has come to call it). The Almagest is massive and obviously took Ptolemy years of tedious calculations and trials of different epicycle models before he arrived at the final set he presented.

2. Epicycles are small circular orbits that themselves orbit the Earth at a uniform velocity on large geocentric circular orbits called deferents.

3. The planets orbit on the epicycles at a uniform velocity.

4. Thus, the planets have net motion in outer space that is rather complex.

   However, the complex motion is made comprehensible by being composed of circular motions.

5. Ptolemy---following the lead of Plato (428/427--348/347 BCE)---believed in principle that uniform (i.e., uniform-velocity) circular motions had be the elementary motions of astronomical objects.

6. Actually, Ptolemy violated the principle of uniform circular motions in his full system by introducing the equant (with its own equant eccentricity) and ---this was crime of Ptolemy.

7. The equant is an empty point in space that is a eccentric by a small distance from the center of the deferents.

   The Earth is eccentric by the same distance from the center of the deferents in the opposite direction.

   The epicycles orbit with uniform angular velocity about the equant---thus they do NOT orbit with uniform velocity about the center of the deferents nor about the Earth.

8. From a modern perspective, it is clear that equant was an attempt to account for the non-uniform elliptical motion of the planets.

   But from the Ptolemy's perspective and those of the other followers of Plato's uniform circular motion principle, the equant was an ad hoc hypothesis that violated the uniform circular motion principle.

   Ad hoc hypotheses are generally deprecated in science.

   They are fudges that may hide the fact that the theory or model in use is actually wrong.

   An ad hoc hypothesis may turn out to be true or may be heuristic hypothesis (i.e., one useful for furthering the investigation), but on the other hand, an ad hoc hypothesis may prevent a researcher from finding the truth or, at least, something closer to the truth.

   This was the case for Ptolemy and his follower up until Nicolaus Copernicus (1473--1543).

9. By adjusting the model parameters (sizes of the epicycles and deferents and the speeds of motion on these---and using the equant), Ptolemy was able to fit the motions of his model to the actual angular motions of the planets (which include here the Sun and the Moon) on the sky to reasonable ancient accuracy.

10. Of course, Ptolemy had the 3-dimensional space arrangements and motions of the planets are mostly wrong.

    Why was Ptolemy so wrong?

    1. The ancient Greek astronomers couldn't measure the distances to the planets except for the Moon---their geometry, but their instruments were weak.

    2. Ptolemy had the wrong model of the Solar System. It's heliocentric, as we know.

11. Another problem with the Ptolemaic system is that it is NOT the uniquely good epicycle model.

    There are a quasi infinity of more or less equally good epicycle models as mathematical astronomers from Ptolemy to Nicolaus Copernicus (1473--1543) went on to show.

12. Despite above criticisms, the Ptolemaic system was a triumph of mathematical astronomy.

    It did allow the prediction of astronomical events to some accuracy as long as its parameters were updated for the current historical epoch.

    Among other things, the Ptolemaic system did reproduce apparent retrograde motions (the westward angular motions of the planets which are deviations from their usual eastward motions) and the planetary configurations.

13. The terms in the applet need some explanation. As needed, just click on any of the keywords given in Ptolemy system keywords below (local link / general link: ptolemy_system_keywords.html):

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