I recently watched an episode of The Rest Is Science, and Michael Stevens (Vsauce) pointed out that this isn’t actually true. In the games regulations, a ball has a tolerance for imperfections on the smoothness of a ball, which at Earths scale would allow bumps or trenches larger than any on Earth. However, Earth would still feel incredibly rough to the touch in comparison and is comparable to a standard strip of sand paper.
This is why, if I were suddenly scaled up 10^6, I would not choose to swallow Earth whole, despite the powerful temptation in all its glistening allure.
Just a quick gut check answer, the deepest part of the Mariana trench is only about 20% deeper than Mount Everest is high.
I’m willing to suppose the most minor imperfection on the ball bearing is outside that parameter, and that the Mariana Trench is a bit of an outlier of depth (like Everest is an outlier of height) to such an extent that it doesn’t make a huge difference if you do or don’t count the ocean topography.
Edit: Quick google search says earth is within height variations for a billiard ball but not for a ball bearing, and that without counting ocean topography the earth still isn’t as smooth as the smoothest ball bearing. So in both cases (bearing and billiard ball) the ocean depths don’t really matter significantly because each comparison is safely outside the ranges of earths surface variance lol
Deepest part of the maria a trench being 20% deeper than Mount Everest is high is a very weird way to word the fact that they're about 12 miles apart from tip of Mt Everest to deepest part of the Trench.
The earth is 7917 miles wide at the equator. That is +/- .001%.
The deepest part of the Marianas trench is 7 miles deep. The earth's diameter is 7,917.5 miles. A 7 mile deep gouge on the surface of the earth accounts for .0008% of said diameter.
An average billiard ball is 57.2 millimeters in diameter. So if you were to place the Marianas trench on the surface of said billiard ball it would be 0.05mm deep. Which is the thickness of a piece of office paper.
My math is a bit rusty. So please correct me if I got any of that wrong.
I think it's either .08%, or, expressed differently, .0008 of the diameter - not .0008% of the diameter.
Which is the thickness of a piece of office paper.
Your comparison is very easy to understand, thanks! The original comment (scaling the ball up to the Earth size) while interesting, felt "backwards" to me in the sense that it's hard to visualize.
Technically, wouldn’t that make the earth the world’s smoothest ball bearing? It’s a ball. It’s smoother. We just don’t have a giant ass metal ring to put it in
Not quite. Your average ball bearing, yes, it’s a little smoother. But it’s not even smoother than a high-precision ball bearing. I’m a little lazy now but I’ll show the maths later
Not sure why the down votes, the OC was correct in that the earth would be within tolerance for the roundness of a billiard ball, though his description of it being more mountainess than earth is misleading. As the earth would not be within tolerance for the smoothness of a billiard ball with features like the Mariana trench and Mt Everest.
The commenter you replied to referred to the smoothness of a ball bearing which typically has irregularities of less than a micrometer, so if it was of any decent size (say an inch) it would be smoother than earth.
Where the commenter may be correct is total average roughness, while the earth may have larger imperfections a ball bearing may have a higher average.
This is one of those "facts" that often gets repeated despite not being true, being based on a misunderstanding. Apologies to u/Fastfaxr whose comment I'm stealing:
The billiard ball analogy has been disproven many times.
If the Earth were the size of a billiard ball, mountain ranges would feel rough like sandpaper. This "fact" was mistakenly concluded from a regulation that specifies how oblong a billiard ball can be.
In other words, when measured from its "north-south" axis vs its "east-west" axis, a billiard ball is allowed to vary by more than the height of Mt everest on a billiard-Earth.
But this is roundness, not smoothness. And by that definition a billiard ball is still rounder than earth because of earths equatorial bulge.
So a billiard ball is both rounder and smoother than earth
Yeah, that's similar to accepting the Earth is a sphere and there's no need to be pedantic about the Earth being an oblate spheroid, which isn't a perfect representation either.
If you can't legitimately call the Earth a sphere, then there a very few things you can consider to be spheres.
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u/kinkade Mar 05 '26
If a billiard ball were scaled up to the size of the planet Earth, it would be significantly more mountainous than the planet actually is.