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xkcd #2898: Orbital Argument
(imgs.xkcd.com)
Alt text:
"Some people say light is waves, and some say it's particles, so I bet light is some in-between thing that's both wave and particle depending on how you look at it. Am I right?" "YES, BUT YOU SHOULDN'T BE!"
I would not call it orbiting if the center is within the body. So, since the center of the sun-Jupiter system is just outside the surface of the sun, I would say the sun and Jupiter orbit the center of their system, but since the center of the sun-earth system is within the body of the sun, I would not say the sun orbits the center of this system. The path the sun takes in this system is entirely contained within its body.
Now, since the sun, Jupiter, and earth are all in the same system, there’s even less reason to say the sun orbits the earth, since the earth has a negligible effect on the sun’s motion.
Just because you believe that a negligible effect means that it shouldn't be called orbiting doesn't change the fact of the matter that there is still a shared gravitational center that both bodies orbit around...
It doesn't matter if it's negligible or not, the fact of the matter is that such a point exists and both bodies orbit around that point.
Then literally everything is orbiting literally everything else, and the word orbit is completely useless.
I have a gravitational effect on the earth. The earth-hperrin system has a gravitational center that both bodies revolve around. Does that mean the earth and I orbit that center? No, because my effect on the earth is negligible. The absolutely immeasurably small wobble my mass gives the earth is not an orbit. There are bodies much more massive than me that the earth orbits (despite how many Doritos I eat).
To put in less hyperbolic terms, Mars’ moon Phobos and Mars have a gravitational center, deep deep deep within the Martian core that both bodies revolve around. Does that mean Mars orbits this point? I don’t think a reasonable person would say so. A massive body wobbling because of a small body orbiting it is not orbiting. Only one thing in such a system is orbiting.