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Epicycles and Planetary Motion

# Epicycles and Planetary Motion - apparent position of the...

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Epicycles and Planetary Motion The "solution" to these problems came in the form of a mad, but clever proposal: planets were attached, not to the concentric spheres themselves, but to circles attached to the concentric spheres, as illustrated in the adjacent diagram. These circles were called "Epicycles", and the concentric spheres to which they were attached were termed the "Deferents". Then, the centers of the epicycles executed uniform circular motion as they went around the deferent at uniform angular velocity, and at the same time the epicyles (to which the planets were attached) executed their own uniform circular motion. The net effect was as illustrated in the following animation. As the center of the epicycle moves around the deferent at constant angular velocity, the planet moves around the epicycle, also at constant angular velocity. The
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Unformatted text preview: apparent position of the planet on the celestial sphere at each time is indicated by the line drawn from the earth through the planet and projected onto the celestial sphere. The resulting apparent path against the background stars is indicated by the blue line. Now, in this tortured model one sees that it is possible to have retrograde motion and varying brightness, since at times as viewed from the earth the planet can appear to move "backward" on the celestial sphere. Obviously, the distance of the planet from the Earth also varies with time, which leads to variations in brightness. Thus, the idea of uniform circular motion is saved (at least in some sense) by this scheme, and it allows a description of retrograde motion and varying planetary brightness....
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