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It leaves out the original definition of planet, the things in the night sky that move.
IIRC, a planet has to clear its orbit (absorb or chase away all rivals) and Pluto can't do that.
I realize there is a mathematical definition of "clear its orbit" which produces the desired conclusion.

However, I happened to be reading about Lagrange points and how objects cluster in the L4 and L5 points and I said to myself "...waaaaait a second, all those planets with Trojan asteroids haven't cleared their orbits in the plain English meaning of the phrase!"

Including Earth, Mars, Jupiter...

You can't prove a definition wrong, but you can make fun of it.

Planet is an arcane term with minimal utility for communicating what you are actually talking about. Whether something is a planet is dependent on not just its own properties, but also the object's location and environment. Something that would be a planet in one location is not elsewhere. The definition of planet is also only applicable to our solar system. Even if you were in orbit around an object, you would not be able to know whether it was a planet or not. It's okay if you are trying to distinguish 8 specific objects from the rest of the universe, but that's about it.

Planemo is a word describing what comes to people's minds when they think planet. A contraction of Planetary Mass Object, it is something large enough to be in hydrostatic equilibrium (round because of its own gravity) but small enough not to fuse elements. You can tell if something is a planemo just by looking at it.

Earth: Planet? Yes. Planemo? Yes.

Pluto: Planet? No. Planemo? Yes.

Earth's Moon: Planet? No. Planemo? Yes.

Earth's Moon if it didn't orbit the Earth: Planet? Maybe. Planemo? Yes.

Mars' Moon Deimos: Planet? No. Planemo? No.

Mars if it had the same orbit as Pluto: Planet? No. Planemo? Yes.

Pluto if it had the same orbit as mars: Planet? Yes. Planemo? Yes.

Hypothetical star in orbit around sun: Planet? Yes. Planemo? No.

Tatooine: Planet? No clue. Planemo? Yes.

Let’s have a talk, Pluto. We know you’ve been feeling blue They changed your class, so you go blame it on the IAU Now you’re a dwarf planet, and you’re not thrilled, it’s plain to see But if you look at what makes a planet great The dwarves have two out of three:

1 You orbit a star, and your star is called the sun 2 You have enough gravity to make you round, but you’re missing one: 3 Do you clear your surroundings? Dwarf planets don’t clear their neighborhood They don’t have enough mass, but join the class If you don’t know their names, you should

Ceres Makemake Haumea Eris Pluto

[0] - https://www.youtube.com/watch?v=ws3kWuMi0Y8

Some say that the reason for demoting Pluto was to avoid admitting Eris to the club of planets while pretending to be consistent. The "clearing your orbit" thing was more of a cover story.

It's possible that Eris took it as a snub. There certainly seems to be a lot of chaos recently.

I’m Eris, and there is no stranger orbit than this, ‘cuz we Bend the rules where I’m at in the Scattered Disc I’ve been hearing some confusion in the past: Pluto may be bigger, but I got more mass
Ceres was a planet, until it wasn't. The reason is they found dozens of objects in similar orbits.

A similar situation exists with Pluto.