Is the earth really smoother than a regulation billiard ball?
I mean regarding the projections on the surface of the earth, not in terms of the earth’s roundness as a sphere.
I imagine, and someone will surely come along in a second with the cite that I am too lazy to look for, that if you enlarged a billiard ball to the size of the earth, it would not be at all smooth.
Likewise, if you shrunk everything on the earth down to the size of a billiard ball, most of the major features would seem to be of regular size, to an earth sized being.
I know this has been asked here before.
The highest point on Earth is Mount Everest, 8 km above sea level. The lowest point on the Earth’s crust is the Mariana, 11 km below sea level. So let’s call the variation 20 km. The radius of the Eath is 6400 km, so the Earth is smooth to 0.3%.
The radius of a billiard ball is 1 1/8 inches, or 2.86 cm. To make a billiard ball as smooth as the Earth, its surface would have to have variations less than 0.0089 cm, or 89 microns.
That said, I have no idea how smooth a regulation billiard ball is.
Coincidentally, 89 microns is about the width of a human hair. I also don’t know how smooth a billiard ball is. Funny how the Earth is the easy part. 
I would be surprised if it wasn’t, but I tried multiple searches and the question didn’t come up in any of the results, except for a couple of people stating it as fact.
One thing you’re missing is that the earth isn’t a sphere, it’s an ellipsoid. The distance along the equator is about 26 miles bigger then from pole to pole. That’s a deviation of almost .7%
I’d be shocked to hear a billiard ball is out of round to the tune of two hair widths. Anything’s possible, but that just seems a huge amount.
What you’re really talking about here is the extent to which the earth and the billiard ball conform to their “nominal” shape (oblate spheroid and sphere, respectively), ie their regularity, which is not necessarily the same as smoothness.
The human finger can detect a peak one human hair wide and tall (a simple test to verify!), so I expect that certain natural features of the earth would feel irregular, sharp, or rough to the touch, albeit for the most part incredibly smooth, were the planet shrunk down to eight-ball scale. It’s thus conceivable that a billiard ball could be more consistently smooth than the earth, whether or not it’s as regular.
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Before every single shipment, all products are carefully inspected and measured to comply the minimum standard on the world-class billiard standard and that listed in BCA (Billiard Congress of America). Ball roundness gauge is used to test the true roundness of every single ball before shipment.
From here: http://www.vigma.com/quality_content.html
So these guys make there balls smooth to about .0127 cm which is not much more than the .0089 cm from Podkayne.
From the Billiard Congress of America equipment specifications (http://www.bca-pool.com/play/tournaments/rules/equip.shtml):
hmmmm. Is it appropriate to compare .005"/1.125" (.44%)? or .010"/1.125" (.89%)?
Also, this is really the accepted tolerance for diameter, not necesarrily smoothness or regularity…
So, I dunno, but there’s some numbers to play with.
That’s why I was wondering in the OP about the smoothness, because the manufacturer’s numbers usually specify the tolerance for the diameter, not the difference between the “peaks and valleys” on ball.
I’ve been involved in a discussion of this subject on alt.fan.cecil-adams a few years ago. My point, and I think it stood, is that the Everest/Mariana bumpiness is very different from the out-of-round spec of a billiard ball. The Earth is also out-of-round, but that’s not what’s being questioned.
The Earth/Mariana bumpiness I figured was equivalent to one sheet of paper’s thickness. So if you take a billiard ball on a smooth surface, and roll it over the edge of a sheet of paper, will there be a noticeable bump to its roll (in other words, is the bump due to the thickness of the sheet much greater than the bumps on the ball itself)?
The answer, which I just confirmed, is yes, the bump due to the sheet of paper is much larger than the ball’s bumpiness, so no, the Earth is not as smooth as a billiard ball.
Only on the SDMB can the width of two human hairs be described as “huge”… 
Why would you use the Everest/Mariana distance, why not Everest/Sea Level? Also we must take into account that Everest and Mariana are on opposite sides, it’s not like you go straight from the peak to the valley, as you would for a bump or scratch in a billiard ball. Everest is quite high, but so is everything else around it, so it might be out of round but still be “smooth”.
For levels that are very close to one another geographically (which would affect smoothness), you’re probably talking a fifth to a tenth of what Pokadyne calculated. My guess is the biggest thing you’d feel would be Mauna Kea, if you went from the sea floor to the peak.
The OP did address this, though.
When this question is asked is it really the dry surface of the earth that is being compared or the surface as is? 
[sup]20 ft. waves are considered pretty rough![/sup]
I think this is a good point. Does anyone have a strict definition of smoothness as it applies to billiard balls? Because then we can apply it to the Earth.
On a kind of related note, I read somewhere that the relationship between the thickness of the atmosphere and the diameter of the Earth is similar to the relationship between the thickness of an apple skin and the diameter of the apple. I think I may have asked about this on the SDMB before, but to my shame, I can’t remember the answer.
Sea level only has any significance to the water, and I think we’re discounting everything except solid rock. Otherwise you’d get a puddle on your billiard table.
CurtC is on track. Try putting a sticker on a billiard ball. It will affect the roll and will be noticable to the touch.
Using the highest/lowest points on the crust seemed best for this kind of back-of-the-envelope calculation for a couple of reasons:
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Sea level is rather arbitrary; it fluctuates as the climate changes. How much liquid water happens to be in the oceans at the present moment doesn’t have much to do with the roughness of the Earth’s solid surface.
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It seemed like an easy way to find out the broadest possible range. If this was much less than the smoothness of a billiard ball, then we would know that the assertion was true.
I agree, however, that it would be more relevant to consider the largest change in relief over a given baseline on the surface of a sphere, but I imagine you could get up to your eyeballs in statistics fairly quickly by considering baselines of various lengths.
It should be borne in mind that as planets go, the Earth is relatively smooth, owing to erosion. IIRC, Mars and Mercury have much greater relief. I think a billiard ball would beat Mars, at least.