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Planet Retrograde Motion: Earth center, Sun-center

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How can planet retrograde motion be explained by the Earth center hypothesis? By the Sun-center hypothesis?

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There is a very good explanation on the web:

http://www.scienceu.com/observatory/articles/retro/retro.html

In a few words, one can summarize as follows: in most cases, planets wander from west to east on the sky, but sometimes they slow down for awhile, stop, move from east to west (this is the retrograde motion), slow down ...

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