By the second quarter of the 17^th century many astronomers accepted the heliocentric theory as reality and not just as useful mathematical fiction.

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The heliocentric theory was first proposed by Copernicus in the 16th century, but it took several decades for it to gain acceptance among astronomers. By the second quarter of the 17th century (i.e. the 1600s), many astronomers had indeed accepted the heliocentric theory as reality.

By the Second Quarter of the 17th Century Many Astronomers

By the Second Quarter of the 17^th Century Many Astronomers