How Galileo Used Mathematics to Prove the Spots Were on the Sun

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Let's describe a sunspot's movement geometrically, as Galileo did: Look at the figure, where the circle represents a view of the Sun from above and "you" represents you, an observer on Earth.

The points A, B, and C are points taken at equal distances on the surface of the Sun, and thus represent positions of a sunspot at equal intervals of time. The apparent motion from A to B, as seen by you, is measured by the angle A-you-B. Compare it to the angle B-you-C, which is obviously much larger. Since the time and distance are the same for A-you-B and B-you-C, the spot appears to move much more slowly as it rounds the edge of the Sun than when it passes across the middle of the disk.

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On the other hand, if the spot were a planet revolving around the Sun, as shown by the black circle, the angles A-you-B and B-you-C differ by only a very small amount.



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Now, can you do a calculation to express these results mathematically?



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Last revised by DKS on May 19, 1997