Quote steeljaw354 (

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It's not that I don't like math, it's that it shouldn't be included in a planet definition.
You don't have to include the math. You can recognize without math that the 8 currently defined planets in our system are very unique in their orbital space, whereas objects like Ceres and Pluto and Eris are not that unique -- they share the region with a lot of similar objects.
The math (easy math -- dividing one number by another number) shows that this difference isn't small. It's huge. Too huge for us to simply ignore.
The harder math shows why that happens. It captures the dynamics of planet formation. That's why it's so useful. That's why this definition works. And, much as you may not like it, this dynamics is orbital-distance dependent. Orbits are faster at smaller distances, so it takes a less massive object to dominate its orbit at smaller distances. This crazy-sounding location-dependent definition comes directly from nature. To dismiss it is to ignore nature.
Quote steeljaw354 (

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The IAU definition says nothing about orbital domination.
Orbital domination and orbital clearing are exactly the same idea expressed in different language. One naturally leads to the other.
Quote steeljaw354 (

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If you cloned mercury and put where every planet is, Mercury-Pluto. And you erased all moons. All of the mercuries would be planets except for the one that is in Pluto's place by your standards.
The planet formation process does not allow an isolated Mercury to form in Pluto's place. Precisely because it isn't massive enough to clear that orbit in solar system timescales. Either the disk at that location must form a more massive planet, or it remains a disk. The definition which you think makes no sense, works.