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I don't know an exact way to measure refraction either, but I can see how it would magnify the size. It surely won't result in the moon measuring the same exact size all across the Earth if the moon is 3,000 miles away. If the moon is 238,000 miles away, it definitely will measure the same exact size from everywhere on Earth.

We have a couple of weeks till a nice full moon to put this to the test!

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