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There is also an argument that the Moon does not orbit the Earth but in fact orbits the Sun with minor influences from the Earth's gravitation. But then, is the Earth a hemisphere supported by four elephants standing on a turtles back?

Glad you mentioned that. I was almost going to include that the Moon is orbiting the Sun too, but thought I'd keep it simple. :-)
This is a great simulation in my opinion.
Not my content, I'm just sharing it here

https://www.youtube.com/watch?v=UgpIy4tUjFI