The video above barely scratches the surface.
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They completely miss mentioning how the moon appears the same in the sky when viewed from the far northern hemisphere to the far southern hemisphere. In the USA today, the moon appears in the early evening sky , low toward the west, as a waxing crescent. It appears that way in the arctic tundra of Canada, all the way south to Tierra del Fuego. It appears low in the western sky with the same portion illuminated by the sun, no matter where on earth you're standing when you see it.
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This fact would not be what we see if the earth were "flat." And the reason is as follows: the earth is not "flat." Simple.
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