The planet’s gravity should dominate its orbit.
All of Jupiter’s moons clearly orbit Jupiter. All of the trojans are gravitationally bound to Jupiter. Jupiter outweighs everything in its orbit by about 5 orders of magnitude
If you look at Pluto, it and Charon orbit a center of gravity outside either of them. Charon is 12% as massive as Pluto, the next highest ratio is Earth’s moon which is just 1.2% the mass of that system. Pluto makes up less than 10% of the mass in the same orbital zone, we only called it a planet because we happened to see it a century ago and didn’t realize that Eris outweighs it out there.
Ceres is probably the best case for “cleared the neighborhood” being a qualitative requirement. Ceres makes up a third of the mass of the asteroid belt, but you probably don’t want to call Ceres a planet because its surrounded by lots of other rocks that really aren’t gravitationally bound to it.
The refinement of the planet definition came about because leaving Pluto as a planet meant we had over a dozen “planets” and potentially 3 in the asteroid belt alone
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