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  > Earth-Moon centre of mass is inside Earth, so, it's
  > obvious that the Moon is orbiting the Earth, not both
  > orbiting something else.
I used to agree with that school of thought, until I came up with a small thought experiment. Consider two bodies that are right on the planet-moon / dual-planet definition threshold. Intuitively, increasing the orbital distance between them would push them in the direction of which definition: planet-moon or dual-planet?

I'd tend to say that separating them further would tend more towards planet-moon. Yet doing so moves the system's center of mass outside the larger body, so would actually push the system into the dual-planet definition by that criterion.



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