Page 19 - GALIET PHYSICS BLOSSOMS I+

2. The epicycle’s velocity on the deferent 3. The epicycle’s radius
4. The deferent’s radius
The apparent retrograde motion can be described and predicted for any planet anywhere in the heavens.
What Ptolemy Does
Ptolemy combines these two forms of epicyclical motions to explain: (1) variations in velocity, and
(2) retrograde motion.
Ptolemy’s Choice between Two Models
At this point, Ptolemy had to choose between an eccentric model and a simple eccentric deferent. Both account for changes in planet’s velocities.
Figure 3.11
Ptolemy was far more interested in a mathematical model than an actual physical one. When Ptolemy recognizes that both Models I and II are mathematically equivalent, Ptolemy chooses the eccentric Model I for simplicity’s sake, however he does not reveal to anyone how he discovered it! What he does reveal is that Model I is still not quite sufficient.
For the eccentric Model I to suffice mathematically, Ptolemy argues that it is not wise to conceive the epicycle’s center to circle the deferent’s center at a uniform rate, for it leads to error. (This was Copernicus’ key objection to Ptolemy’s work).
11 This figure and explanation is drawn from Dr. Robert A. Hatch’s
h t t p : / / w w w . c l a s . u fl . e d u / u s e r s / u fh a t c h / H I S - S C I - S T U D Y - G U I D E / 0 0 3 4 _ s u m m a r y P t o l e m i a c A s t r o n . h t m l
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