Maybe you’ve heard this statement: if the Earth were shrunk down to the size of a billiard ball, it would actually be smoother than one. When I was in third grade, my teacher said basketball, but it’s the same concept. But is it true? Let’s see. Strap in, there’s a wee bit of math.
OK, first, how smooth is a billiard ball? According to the World Pool-Billiard Association, a pool ball is 2.25 inches in diameter, and has a tolerance of +/- 0.005 inches. In other words, it must have no pits or bumps more than 0.005 inches in height. That’s pretty smooth. The ratio of the size of an allowable bump to the size of the ball is 0.005/2.25 = about 0.002.
The Earth has a diameter of about 12,735 kilometers (on average, see below for more on this). Using the smoothness ratio from above, the Earth would be an acceptable pool ball if it had no bumps (mountains) or pits (trenches) more than 12,735 km x 0.00222 = about 28 km in size.
The highest point on Earth is the top of Mt. Everest, at 8.85 km. The deepest point on Earth is the Marianas Trench, at about 11 km deep.
Hey, those are within the tolerances! So for once, an urban legend is correct. If you shrank the Earth down to the size of a billiard ball, it would be smoother. But would it be round enough to qualify?