Stern headed up the New Horizons project. He also coined the term dwarf planet.
Wikipedia’s article on dwarf planet, covers both hydrostatic equilibrium (roundness) and orbital dominance. (Unfortunately, for the hydrostaticists, it’s easier for an icy body to get round, and harder for a rocky body).
We’re at the stage where you are pointing me to things I already explicitly talked about in more detail. I’mma finish here then, if it’s all the same to you. 
https://www.nasa.gov/mission_pages/lucy/overview/index
An upcoming mission, launching in October 2021, to investigate the L4 and L5 trojans of Jupiter. The orbital trajectory is really something.
There’s a rival nomenclature for planets-- something that Alan Stern has proposed.
A planet is a sub-stellar mass body that has never undergone nuclear fusion and that has sufficient self-gravitation to assume a spheroidal shape adequately described by a triaxial ellipsoid regardless of its orbital parameters.
Notably this definition includes Europa (even prior to the events of 2010), and would exclude Lucifer.
At present, there are 110 “geophysical” planets, and some of them were previously classified as moons.
and what about our moon? ive heard that it’s orbit can be explained either as rotating around us, or as twisting with us around the sun…
planets enough for everyone! 
i think there’s a real debate about what taxonomies even are. grouping species by evolutionary divergence is but one method, and im not sure that everyone even agrees about that
ultimately i think they’re like maps. there are probably different useful maps of the same set of stuff used for different purposes depending on what the question is
( im not sure darwin, for instance, even believed in species. as there are tons of exceptions to the easy seeming rule of successful interbreeding offspring. nature is messy, our categories imperfect always. )
If the barycenter lies outside the radius of the larger object, it’s a double planet. If not, it’s a planet and a moon.
i think the argument is that the sun has a larger attractive force on the moon than the earth does, and so it’s possible to model us as a binary planet… which is different than all the other things we call moons in the solar system
there’s a little bit on the wikipedia page about the specialness of the moon’s orbit even if it’s not nearly as heretical as my foggy memories
A version of this question was asked at the 1h54m mark
Very long. Entertaining.
At an earlier point in the debate, my “concerns” over the downgrading of planets leading to diminished interest among budget allocators were dismissed, so I guess that’s egg on my face.
bookmarking for later. thanks!
The IAU treatment is just one view in an ongoing debate. It is not gospel truth. The scientist who coined the term “dwarf planet,” Alan Stern, intended it to refer to a subclass of planets. Dwarf planets are not at all like asteroids. Dwarf planets are rounded by their own gravity; are geologically differentiated into core, mantle, and crust, and have active geology and weather. In contrast, asteroids are rubble piles that are shapeless and loosely held together by chemical bonds.
Planetary scientists who support the geophysical definition consider Ceres to be a planet because it is in hydrostatic equilibrium. This is discussed in many publications that address planet definition. The reason most planetary scientists favor the geophysical definition is that they focus on the intrinsic properties of celestial objects rather than their locations or influences on other celestial objects.
In this article, planetary scientist Kirby Runyon presented the geophysical definition to the 2017 Lunar and Planetary Sciences Conference: https://www.hou.usra.edu/meetings/lpsc2017/eposter/1448.pdf
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