You may have heard it has been said that if the Earth were shrunk down to the size of a billiard ball, it would be smoother than it. In other words, the Earth is smoother than a billiard ball. Is that true?
Back in 2008, on the “Bad Astronomy” blog on discovermagazine.com, in the article titled “Ten things you don’t know about the Earth“, Phil Plait wrote about that, and said “…according to the World Pool-Billiard Association, a pool ball is 2.25 inches in diameter and has a tolerance of +/- 0.005 inches.” and after making some calculations, he concluded that “… the urban legend is correct. If you shrank the Earth down to the size of a billiard ball, it would be smoother.”
Even the famous American astrophysicist, author, and science communicator Neil deGrasse Tyson once tweeted about that, saying “If shrunk to a few inches across, Earth would feel as smooth as a billiard-hall cue ball.”. (You can see his tweet here)
Smoothness vs roundness
In fact, the Earth is much smoother than one might think. It definitely would NOT look like this without water, for example. Yes, there are big mountains like the Himalayas and big trenches under the oceans like the Mariana Trench.
The highest point on Earth is the top of Mount Everest, at 8.85 km. The deepest point on Earth is the Mariana Trench, at about 11 km deep. But even those are very small compared to the Earth’s diameter which is about 12,735 kilometers (on average).
According to the World Pool-Billiard Association, “All balls must be composed of cast phenolic resin plastic and measure 2 1/4 (±.005) inches [5.715 cm (± .127 mm)] in diameter”.
So, if we could shrink the Earth to the size of a billiard ball, the height of Mount Everest would be only 0.04 millimeters. The depth of the Mariana Trench would be only 0.045 millimeters. These measurements are inside the tolerance of 0.127 mm or 0.005 inches, with no pits or bumps more than that, so the Earth is smoother than a billiard ball, right?
Wrong.
First of all, the specifications of
Let’s assume that we produced a billiard ball and covered its surface with a medium sandpaper (grit particle size of 0.005 in, for more about grit sizes of sandpaper see the Grit size table on the Wikipedia entry of sandpaper). By the definition of smoothness used by Phil Plait of Discover Magazine and Neil deGrasse Tyson, that billiard ball would also be “smooth” – which is obviously ridiculous.
The billiard-ball-sized Earth’s smoothness would be equivalent to that of 320-grit sandpaper. Still not quite smooth, right?
So, it’s obvious that 0.005 inches (0.127 mm) official tolerance is for shape, for roundness, not for smoothness.
Human fingertips are very sensitive
According to a 2013 study titled “Feeling Small: Exploring the Tactile Perception Limits” published in Nature, a human finger can feel wrinkles as small as 10nm (nanometers), or 0.00001 millimeters, demonstrating that human tactile discrimination extends to the nanoscale.
So, if the Earth were shrunk down to the size of a billiard ball, you would definitely feel Mount Everest, which would be 0.04 millimeters high. You could actually feel most of the highest mountains in the world.
Why Earth is not as smooth as a billiard ball? Dr. James O’Donoghue’s explanation
JAXA (Japan Aerospace Exploration Agency) scientist Dr. James O’Donoghue also tweeted about why Earth is not as smooth as a billiard ball. You can see the thread here.
Dr. James O’Donoghue uses the bowling ball to scale, but what he says is still valid for the billiard ball.
How smooth is Earth?
Earth’s highest/lowest points are 8.9km (Mount Everest)/-11 km (Mariana trench), but let’s assume a local variability of 1 km for now.
If Earth were shrunk to bowling-ball width (21.6 cm), then 1 km bumps represent 0.017 mm: about the particle size of P1000 superfine sandpaper!
If you thought 1km was too much variability, try 0.5km: P2500 Ultrafine sandpaper, particle size 0.0084mm
Mount Everest is 8.9 km above sea level and would be about half the size of a grain of salt (0.15 mm) at the scale of this bowling ball, albeit with a wide base.
So, perhaps Earth isn’t as smooth as a brand-new glossy bowling ball, but it’s not very rough either.
Something to end on: Earth’s oceans would be one-third the height of a grain of salt on the scale of a bowling ball, a film so thin your hands would barely get wet holding it.
Earth is as round as a billiard ball (but still it would make a terrible billiard ball)
Speaking of roundness, is Earth as round as a billiard ball?
Earth’s equatorial diameter is 7,926 miles (12,756 km), but from pole to pole, the diameter is 7,898 miles (12,714 km) – a difference of only 28 miles (42 km).
If we take the bigger diameter and shrink it down, the difference would be 0.0049 inches (0.0125 mm). If we take the smaller diameter, the difference would be very slightly bigger, but almost the same. So yes, the Earth is as round as a billiard ball. But it’s almost at the limit.
Dr. David Alciatore, Ph.D., writes:
“The Earth would make a terrible pool ball. Not only would it have a few extreme peaks and trenches still larger than typical pool-ball surface features, but the shrunken-Earth ball would also be terribly non-round compared to high-quality pool balls.”
“The diameter at the equator (which is larger due to the rotation of the Earth) is 27 miles greater than the diameter at the poles. That would correspond to a pool ball diameter variance of about 7 thousandths of an inch. Typical new and high-quality pool balls are much rounder than that, usually within 1 thousandth of an inch.”
Summary
- Is Earth as smooth as a billiard ball? Answer: No.
- Is Earth as round as a billiard ball? Answer: Yes, it is within the limits, but still it would make a terrible, terrible billiard ball.
You can also watch Vsauce’s great video titled How Much of the Earth Can You See at Once? which also covers this very subject.
As you can see in the video above, as microscopic photography has shown, imperfections on a billiard ball are only 1/100,000 inches, or about 0.5 μm deep and high. Scaled down to the size of a billiard ball, Earth’s Mariana trench would be 49 μm deep.
Let’s think of it in another way: If a billiard ball was scaled up to Earth-size, the difference between the highest peak and lowest point would be about just 223 meters (732 feet) at maximum. A billiard ball is way smoother than the Earth.
Sources
- Ten things you don’t know about the Earth, “Bad Astronomy” blog by Phil Plait on discovermagazine.com
- World Pool-Billiard Association Equipment Specifications on wpapool.com
- Is Earth as smooth as a billiard ball? on skeptics.stackexchange.com
- Is the Earth Like a Billiard Ball Or Not? on Possibly Wrong blog
- “Is a Pool Ball Smoother Than the Earth?” by David Alciatore, PhD
Since you’re talking about Earth and billiards, I’d like to point out that Earth is about 3400 times flatter than a regulation pool table. (Calculating the bulge of a 4′ x 8′ section of a sphere with radius of 6371 meters gives 146 nanometers compared to requirement of +/-0.5mm per WPA & BCA)
I love saying it – The Earth is flatter than a pool table!
Thanks, Dave! Great comment and you’re right 🙂
Next question:
Is earth as smooth as a 4.5 billion year old used cue ball?
I am curious, I’m not 100% sure how all of this works so i could be wrong but the measure of smoothness is also related to the proximity of these height differences right? So your sandpaper example implies that the highest and lowest points of the planet repeat over and over again outwards from a single point(up, down, up, down, up, down) . There is only one point that is the highest and another point that is the lowest with some distance in between, it’s not like there is a mountain and trench tangent every x amount of distance consecutively. The rest of the height differences in the geography are much smaller over a larger area. Am I not thinking of this correctly? This is a really cool idea whether its true or not =)
Hi,
Thanks for the comment. For some places in the world, you’re right. But a lot of other places, there are big differences in elevation. The Himalayas is just an example, also the Alps. For instance, Nanga Parbat’s Rupal Face rises approximately a whopping 4,600 meters, or 15,000 feet, above its base. You would definitely feel it if the Earth were shrunk down to the size of a billiard ball.
The article also fails by using the lowest point as the bottom of the ocean. The ocean is part of Earth, and when shrinking down the Earth shape for a comparison to a billard ball, you would want to consider the whole shape as made from material of a billard as well, or at least solidified, or you would displace the ocean by rubbing your finger over it.
For an accurate representation of Earth’s shape, which in fact includes the oceans, where a larger percentage of Earth’s surface is the surface of the ovean and not landmasses, you can only go from sea level when over the ocean. The lowest point can be an area on land below sea level, but cannot be a spot on the bottom of a body of water or you invalidate your claim.
Thanks for the comment. Even if we take the sea level at the lowest point, the Earth is still not as smooth as a billiard ball.
I heard Neil deGrasse Tyson state this claim on Joe Rogan last week – that the earth, if shrunk to the size of a billiard ball, would be as smooth as one. I had not heard this before. My immediate reaction was, NO WAY. It appears I was correct!
Thanks for the comment, Richard. Yes, you were correct. It is weird that he still states this claim.
He still makes that claim because he is more of a hack looking for media attention than a real scientist
Yes, unfortunately.
If we are talking about a nice new shiny pool ball, I would agree. But compare that with the average one you pick up in a bar and it would be significantly more rough.
The largest deformation on earth from its base is Mauna Loa which rises 5000m from its base. This is around 0.0008 of its radius.
Compare that with a hair on a billiard ball.
A hair is on average 75 microns or or .003″, which then divided by 1.25″ it becomes 0.0024 of its radius. A hair on a billiard ball is 3 times higher than the greatest deformation on the surface of the earth.
A particle of dust is about 10 microns (.00039″) so what we are looking at is effectively a dusty pool ball with a few places two pieces of dust high, and a few scratches 3 parts of dust deep.
For all reasonable arguments I would call that as smooth.
This is nonsense. 14 meters? Funny because that also happens to be the same fact associated with the worlds roundest object -https://www.youtube.com/watch?v=ZMByI4s-D-Y&ab_channel=Veritasium
So are you telling me, an ordinary cue ball is as smooth as the worlds roundest object? AKA billiard balls are also the worlds roundest object LOL Surely not.
I guess I’m not allowed to post youtube links here but if you search “worlds roundest object”, you’ll see why this article is nonsense because it claims in the last paragraph, that an ordinary billiard ball is as smooth as the worlds roundest object. The 14 meters between the tallest mountain, and deepest valley is how smooth that object would be if it were earth sized. No way in hell a billiard ball is just as smooth as an object that cost millions to make, and made to be perfectly round, smooth, and exactly 1 kg
Hi, Hugo. Thanks for the comment. You’re right, sort of. I made an arithmetical error. But a billiard ball is still way smoother than the Earth.
Earth is rounder than a billiard ball, I already mentioned that in the article, and that “world’s roundest object” is rounder than Earth. I think there’s no problem here.
Diameter of Earth 12,742,000 meters
Diameter of a billiard ball 0.05715 meters
Mariana trench 11,000 meters
Everest 8,848 meters
Mariana + Everest = 19,848 meters
If the Earth scaled down to a billiard ball size, the difference between the Mariana Trench and Mount Everest would be about 89μm. This is way bigger the imperfections on a billiard ball (0.5 μm). A billiard ball is still way smoother than Earth.
As you pointed out, I made a mistake while calculating the differences if a billiard ball was scaled up to the size of Earth.
Imperfections on a billiard ball: 0.5 μm. Let’s multiply that with 2, we now have 1 μm of difference between the lowest and highest point.
if we have 1 μm difference on a ball with a diameter of 0.05715 meters,
How many meters difference we would have on a ball with a diameter of 12,742,000 meters?
0.000001 meters -> 0.05715 meters
x -> 12,742,000 meters
x = 12,742,000 * 0.000001 / 0.05715
x = 223 meters
If a billiard ball was scaled up to Earth size, the difference between the highest peak and lowest point would be about just 223 meters at maximum. A billiard ball is still way smoother than the Earth. But the difference is more than 14 meters, you’re right (I fixed the article, thanks for pointing that out).
Why are you discounting Earth’s oceans and atmosphere? They are the planet too.
I see a problem in your logic.
A billiard ball is only the solid part of it.
However, the Earth is NOT only the solid part of the crust. If you discount liquids and gasses that make a planet… then Earth would only be a thin shell (you would remove the magma from the mantle too).
Jupiter and Saturn would cease to exist, as they are mostly gas which slowly becomes liquid towards their cores, due to pressure.
Earth IS covered in water (which makes it even more smooth all around… with bumps only on the patches with continents.
The comparison with grit paper is not apt there too, because the grit size is constant across the grit paper, while on Earth, only tiny patches would have mountains comparable in size with the grit size.
But then, you must also cover the Earth in atmosphere, which IS a part of the planet.
And that is very smooth. Smoother than a billiards ball.
It’s interesting you failed to mention the largest deviation from roundness of the planet — “The Earth has a rather slight equatorial bulge: it is about 43 km (27 mi) wider at the equator than pole-to-pole, a difference which is close to 1/300 of the diameter. If the Earth were scaled down to a globe with diameter of 1 meter at the equator, that difference would be only 3 millimeters. While too small to notice visually, that difference is still more than twice the largest deviations of the actual surface from the ellipsoid, including the tallest mountains and deepest oceanic trenches.” If you’re going to be pedantic, be sure to cover all the bases. https://en.wikipedia.org/wiki/Equatorial_bulge
This is what I came to say! Thank you.
This entire analysis hinges on using a brand new billiards ball.
Sorry but any billiards ball used any extensive period of time will have more bumps and gouges than the earth. If you want to use a new billiards ball as your comparison you need to use a new earth when it was still partially molten at 4.5 billion years ago.
Your average person picking up a regular billiards ball will almost certainly have more gouges and imperfections than the current earth miniaturized.
If the Earth was covered with mountains yes, but it isn’t. Most areas are quite flat, and hills and mountains do not look like grains of sand like on sandpaper. The base of a hill can be 10 times its height, so it’s not comparable to sandpaper like that. The slopes on Earth would be what you’re actually feeling, and they are generally very gradual. You really wouldn’t be able to feel a change if the Earth was the size of a billiard ball for most parts of the Earth. https://billiards.colostate.edu/bd_articles/2013/june13.pdf
For some parts, maybe yes, you wouldn’t feel it. But overall, a billiard ball is much smoother than Earth. Even the link you provided says: “Regardless, the Earth would make a terrible pool ball. Not only would it have a few extreme peaks and trenches still larger than typical pool-ball surface features, but the shrunken-Earth ball would also be terribly nonround compared to high-quality pool balls”