Is Earth as smooth as a billiard ball? No, here’s why

You may be heard it has been said that if our planet were shrunk down to the size of a billiard ball, it would be smoother than it. In other words, the Earth is smoother 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 he 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 “… 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.”.

Earth as a billiard ball
Is Earth as smooth as a billiard ball? Probably not.

In fact, the Earth is much smoother than one might think. Yes, there are big mountains like Himalayas, and big trench under the oceans like 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 a 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 Mariana Trench would be only 0.045 millimeters. These measurements are inside 0.127 mm or 0.005 inches, no pits or bumps more than that, so the Earth is smoother than a billiard ball, right?

Wrong.

First of all, the specifications of World Pool-Billiard Association does not say “there mustn’t be pits or bumps more than .005 inches”. This is only about diameter, the rule says the diameter must be within 2 1/4 (+.005) inches. Smoothness is a very different thing.

Let’s we assume that we produced a billiard ball and covered its surface with medium sandpaper (grit particle size of 0.005 in, for more about grit sizes of a 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 “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 smoothness.

320 grit silicon carbide sandpaper
The billiard-ball sized Earth’s smoothness would be equivalent to that of 320 grit sandpaper. Image: “320 grit silicon carbide sandpaper, with close-up view” on wikipedia.

As round as a 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.

Summary

  1. Is the Earth as smooth as a billiard ball? Answer: No.
  2. Is the Earth as round as a billiard ball? Answer: Yes.

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.

Sources

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