Page 22 - GALIET PHYSICS BLOSSOMS I+

In Ptolemy’s final model, planet P travels uniformly around its epicycle
while the center of the epicycle on its deferent travels uniformly around the equant Q. In this way, regular motion is maintained!
The epicycle center now
circulates around the new deferent
at a constant angular velocity around the equant Q
In other words, the object’s speed varies in its orbit around the circle: It moves faster in the bottom half, slower on the top half.12
The motion is uniform only in that the red object sweeps out equal angles in equal times from a reference point inside the circle.13
The object’s speed is non-uniform from the perspective of the equant point, the center of the equant circle, and the center of the earth.14
Figure A.15
Sequences of Figure B.16
Comparison of the 3 Models of Circular Motion17 Uniform or CentricàYellow Object (Apollonius of Perga) EccentricàGreen Object (Hipparchus) EquantàRed Object (Ptolemy)
12 From http://faculty.fullerton.edu/cmcconnell/Planets.html
13 From http://faculty.fullerton.edu/cmcconnell/Planets.html
14 From http://faculty.fullerton.edu/cmcconnell/Planets.html
15 Figure A was taken from Dr. Stamp’s Slides on Greek Astronomy.
16 Sequences of Figure B and their explanations were taken from http://faculty.fullerton.edu/cmcconnell/Planets.html. 17 From http://faculty.fullerton.edu/cmcconnell/Planets.html
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