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# Is it true that if a highly polished billiard ball was expanded to equal the Earth in size it would have higher mountains and deeper trenches than the Earth?

Question #121443. Asked by unclerick. (May 17 11 9:52 PM)

serpa

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?

 May 17 11, 10:25 PM
davejacobs

This extract "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" seems to be quite wrong. Surely the 'tolerance' in the standard refers to variations in diameter, and has nothing whatever to do with the smoothness. In other words a ball must be between 2.245 and 2.255 inches diameter. If smoothness were an issue, it would presumably be the subject of another standard, but as there doesn't seem to be one we cam tell nothing about pits and bumps from this source.

 May 18 11, 7:38 AM
Baloo55th

I agree with dave that a tolerance in diameter doesn't mean bumps. A difference in diameter is overall, not here and there. I must confess here to a former professional involvement with plastic balls. For a time I worked for a manufacturer of strange plastic things (gully boots, runway clips, barrel skirts, diddymen, and so on). One item was a plastic ball that had to spin without wobbling when it had been made and cooled down. Same principle applies to a billiard/snooker/pool ball. Bowls (flat-green and crown-green) are deliberately asymmetrical but billiard/snooker/pool balls have to be symmetrical. I can just imagine the reaction of a pro to seeing a carefully hit ball behaving as though it were a mini rugby ball...
http://en.wikipedia.org/wiki/Bowls http://en.wikipedia.org/wiki/Snooker

 May 18 11, 4:30 PM

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