Oddbean

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 There are "moons" that appear to orbit around other celestial bodies. The main celestial bodies all appear to orbit around the Earth though. La Grange point probes made the same observations... 3 times. Earth is at the centre of it all.

https://m.primal.net/HZDT.png

https://m.primal.net/HZDS.png

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 Therefore you accept that at least not everything in the universe is earth-centric.

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 All observations ever made would disagree with that assertion, but roll with that.

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 I don't think we're talking the same. 
If a moon orbits Jupiter, and Jupiter orbits Earth (somehow), then the moon, let's say Europa is orbiting Jupiter directly, not Earth. 
It would go around the Earth only indirectly, thanks to Jupiter. 

Is that clear? The "CENTER" for that moon, Europa, is Jupiter. It's a Jupter-centric orbit. 
And you said that's the case.

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 Yet even though that moon is orbiting Jupiter, it is still orbiting the earth on a larger scale, since it follows Jupiter in its orbit around the earth.

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 To that moon, to whoever is living there (if there's anyone living there), they are orbiting Jupiter. 

What matters here is the definition of the word "orbit". The curly salad drawing that you presented is not orbits.

Europa going around Jupiter is an orbit. A simple, curved line around another larger object.