re: So, what are the chances that the moon is the perfect size and distance from earth

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It's only perfect for the people under the shadow.

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The diameter of the moon is "perfect" or very close to perfect for everyone all the time. It's just that it only aligns with the sun perfectly for people in the path during a total eclipse.

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If the moon were bigger their would be a wider shadow.

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yep, but that wouldn't perfectly block the sun with a diameter that is basically the exact same size of the sun. It would block the sun with a much larger area.