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Is there a general term for epicycles, deferents, and eccentrics in Ptolemaic astronomy?

According to Ptolemy's (c. 150 CE) account of the motions of planets, planets moved in circular paths ("epicycles") around center points that in turn moved around the center of the earth along a path ...
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How was Henrietta Leavitt's discovery important for star measurement?

Henrietta Leavitt discovered a relation between luminosity and period of variable stars, so it was possible to measure distance between two variable stars. I am curious to know how that was important ...