Peter

There's an article in Vox on Pluto, and there were some graphs where I thought, "log scale, dammit!"

So I found the masses of planets, and known dwarf planets of known mass, and did a plot:

Note that the x-axis is on a linear scale - not a log scale. With a log scale you don't get a nice straight line - not really. You can fit it to a power law but the fit isn't nearly so good, and there's obvious curvature:


Thing is, lots of things fit power law distributions like this. Most famously, words. But also, asteroids. Kuiper Belt Objects are harder to observe than asteroids but the same power-law statistics might apply to them too. So there's something different between "big 8 planets + dwarf planets" as a group and asteroids as a group, or KBOs as a group.

Note that the exponential law fits better than the power law if you exclude the dwarf planets too - it's not an artefact of welding two groups of dissimilar objects together. Likewise I only have four data points so take this with an astronomical quantity of salt, but the exponential fits the dwarf planets alone better than the power law - and the power law fits better if the objects have ranks 9, 10, 11 and 12 rather than 1, 2, 3 and 4. So "big 8" planets and dwarf planets fit together nicely as a group.

Of course, by contemporary definitions of "planet", this is all irrelevant - they have to have cleared their orbits. However, maybe the current definition isn't the best definition, and maybe one that includes dwarf planets "carves nature at the joints" better.

Incidentally, the data I collected from Wikipedia:

	Rank	Mass
Jupiter	1	317.8
Saturn	2	95.2
Neptune	3	17.2
Uranus	4	14.6
Earth	5	1
Venus	6	0.82
Mars	7	0.11
Mercury	8	0.06
Eris	9	0.0028
Pluto	10	0.0022
Senda	11	0.00022
Ceres	12	0.00015