The moon's orbit probably isn't what you think

From youtube:
We think of the moon as orbiting the earth, following a spiraling trajectory as the earth itself orbits the sun. But this is wrong. Not only is the moon's orbit NOT a spiral... there's an argument that the moon actually orbits the sun, not the earth! The moon's trajectory is more like a 12-sided polygon with curved corners than it is a spiral or even a wiggly line.
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