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I am not sure whether the ancient Greeks were involved. In any case, any movement of the Earth should be reflected in the apparent motion of distant objects, such as stars.However, in practice, this apparent motion is very small for the stars - the yearly parallax for even the closest stars is less than one arc-second (1/3600 of a degree).

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Q: Why did the fact that stars not show any Parallax motion convince the Greeks that the Earth was not moving?
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