What-If 0046: "Bowling Ball"

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What-If 0046: "Bowling Ball"

Postby rhomboidal » Tue May 21, 2013 8:43 am UTC

"I've been told that if the Earth were shrunk down to the size of a bowling ball, it would be smoother than said bowling ball. My question is, what would a bowling ball look like if it were blown up to the size of the Earth?"

—Seth C.


http://what-if.xkcd.com/46/

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Now I want to know, if you similarly scaled up a bowling alley rental shoe, would the teeming noxious germs inside it be the size of Chitauri?

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Re: What-If 0046: "Bowling Ball"

Postby Quicksilver » Tue May 21, 2013 8:47 am UTC

The Big Lebowski <3

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Re: What-If 0046: "Bowling Ball"

Postby jpgsawyer » Tue May 21, 2013 9:05 am UTC

So my question.... how does one assess the loads on the finger holes to workout how quickly they close up?

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Re: What-If 0046: "Bowling Ball"

Postby ijuin » Tue May 21, 2013 9:14 am UTC

rhomboidal wrote:Now I want to know, if you similarly scaled up a bowling alley rental shoe, would the teeming noxious germs inside it be the size of Chitauri?


Let's assume that the shoe in question is 30 cm long (i.e. slightly larger than the median man's foot). The Earth is approximately 1.28 * 10^7 meters in diameter, so let's use that as the length of our planet-sized shoe. This represents an enlargement factor of about 42 million.

Now, a typical bacterium is about 2-3 microns long. Multiplied by 42 million, the bacteria will be from eighty to more than a hundred meters in length--at least twice as long as the longest dinosaurs yet discovered.

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Re: What-If 0046: "Bowling Ball"

Postby Klear » Tue May 21, 2013 9:41 am UTC

ijuin wrote:
rhomboidal wrote:Now I want to know, if you similarly scaled up a bowling alley rental shoe, would the teeming noxious germs inside it be the size of Chitauri?


Let's assume that the shoe in question is 30 cm long (i.e. slightly larger than the median man's foot). The Earth is approximately 1.28 * 10^7 meters in diameter, so let's use that as the length of our planet-sized shoe. This represents an enlargement factor of about 42 million.

Now, a typical bacterium is about 2-3 microns long. Multiplied by 42 million, the bacteria will be from eighty to more than a hundred meters in length--at least twice as long as the longest dinosaurs yet discovered.


So.. a bit larger than the Chitauri leviathans, then.

BTW, I clicked the first link in the What If, read the article there and clicked on the link about centrifugal force, which brought me to an article linking back to xkcd. Cool. The internet is a small place.

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Re: What-If 0046: "Bowling Ball"

Postby cellocgw » Tue May 21, 2013 2:31 pm UTC

I suspect a lot of people have made the "seas of moon <--> bowling ball holes" association over the years. Except in New England, where most of us play that weird Candlepins version. Also, Randall's ninja'd by an article in AIR about Kansas and a pancake.
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Re: What-If 0046: "Bowling Ball"

Postby Barstro » Tue May 21, 2013 3:12 pm UTC

But what advances in polishing technology have occurred since the phrase was first used? Was a bowling ball in the 50's less smooth than the earth?

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Re: What-If 0046: "Bowling Ball"

Postby Moose Anus » Tue May 21, 2013 5:03 pm UTC

Barstro wrote:But what advances in polishing technology have occurred since the phrase was first used? Was a bowling ball in the 50's less smooth than the earth?

I polish balls, and I vote!
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Re: What-If 0046: "Bowling Ball"

Postby Mikeski » Tue May 21, 2013 10:58 pm UTC

I think he needs to show us how the offset weight blocks in Lebowski affect its path around its star, as well.

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Or (whatifwetriedmorepower) how they'd cause the whole planet to fly apart. :mrgreen:

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Re: What-If 0046: "Bowling Ball"

Postby Eternal Density » Tue May 21, 2013 11:34 pm UTC

I'd only heard that if the Earth were shrunk down to the size of a basketball, it would be smoother than said basketball.
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Re: What-If 0046: "Bowling Ball"

Postby blowfishhootie » Wed May 22, 2013 3:42 am UTC

Eternal Density wrote:I'd only heard that if the Earth were shrunk down to the size of a basketball, it would be smoother than said basketball.


This is what I've heard before too. No idea if it's truer than the bowling ball one, but it certainly seems more likely to be true.

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Re: What-If 0046: "Bowling Ball"

Postby ijuin » Wed May 22, 2013 4:27 am UTC

Well, the difference between the Earth's highest and lowest elevations (discounting the planet's oblateness) is only about 20 km, and the planet itself is about 12,800 km in diameter, so that means that the difference is only about two parts in one thousand.

An NBA regulation basketball is approximately 24 cm in diameter. An Earth shrunk to this scale would thus have a difference between its highest and lowest elevations of a mere 350-400 microns. I'm pretty sure that the recessed ribs on a regulation basketball are deeper than two-fifths of a millimeter.

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Re: What-If 0046: "Bowling Ball"

Postby Copper Bezel » Wed May 22, 2013 5:19 am UTC

Damn. Ninja'd to hell while doing another thing. I was looking at the little nubs, though, not the ribs. If they're around a half millimeter, as you say, they would have a greater difference in height than the one between the peak of Everest and the bottom of the Marianas Trench (~25 compared to ~20 km.)

Of course, taking the tact from the What If would mean that the ball would also immediately shred and collapse under its own gravity into a hot ball of chemical soup, liberating a planet-sized ball of air pressurized to four atm that it wouldn't have remotely the gravity to retain. = )

Actually, what would a ball of air 1,000 times more massive than Earth's atmosphere actually do? (Or from another angle, a ball of air with 1/4500 the mass of Earth itself.)

Edit: Disperse, apparently. A fun calculation with a slightly unsatisfying answer.
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Re: What-If 0046: "Bowling Ball"

Postby snowyowl » Wed May 22, 2013 9:13 am UTC

Copper Bezel wrote:Edit: Disperse, apparently. A fun calculation with a slightly unsatisfying answer.

What if we tried more power?

A ball of air the size and density of the Sun would form... well, the Sun. The fact that it's formed of oxygen and nitrogen rather than hydrogen would be a bit odd, but stars can burn oxygen for a while.
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Re: What-If 0046: "Bowling Ball"

Postby robbak » Wed May 22, 2013 12:31 pm UTC

Copper Bezel wrote:Of course, taking the tact from the What If would mean that the ball would also immediately shred and collapse under its own gravity into a hot ball of chemical soup, liberating a planet-sized ball of air pressurized to four atm that it wouldn't have remotely the gravity to retain. = )


There would be a chance that the basketball could remain intact. The standard pressure for a basketball is 8 PSI, air pressure is only 14, so if well built, it could perhaps hold that pressure. The huge amount of air would soon begin compressing under its own gravity perhaps even liquifying, reducing the pressure, if the ball can withstand the initial pressure for an hour or so. Of course, the air would also get hot. Hmm.

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Re: What-If 0046: "Bowling Ball"

Postby Copper Bezel » Wed May 22, 2013 5:22 pm UTC

A regular-size basketball could probably survive in space, since atmospheric pressure is, as you say, a fraction of the difference between the internal and external pressures when it's on Earth anyway, but I wasn't concerned about the pressure difference; even ignoring the air it might be trying to trap, the basketball would have next to nothing holding it together. The square-cube law says that the cross-sectional size (and thus the strength of the materials) has gone up by only 2.7 * 10^15, while the mass has gone up by 1.4 * 10 ^ 23.

Obviously, it's in space, so it's not like a structure on Earth holding its shape against Earth's gravity; its own mass would be a bit over 1/100 of Earth's, which scales directly to 1/100 g at the surface, where the actual materials of the basketball's shell are. But taking the two numbers above into account, that means that the gravitational force on any one part of the ball has still gone up by 5 * 10^5 times more than the material strength has. I don't see a basketball holding together under 500,000 times the forces it normally sustains - even for an hour.

The pressure of the air is still just your 80 psi, so I'm not really seeing it as a factor, but it wouldn't help. = )
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Re: What-If 0046: "Bowling Ball"

Postby snowyowl » Wed May 22, 2013 8:25 pm UTC

So... it would develop a leak and collapse under gravity to form a rough sphere of rubber at the centre of a rapidly dispersing atmosphere?
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Re: What-If 0046: "Bowling Ball"

Postby Copper Bezel » Wed May 22, 2013 9:23 pm UTC

I think so, yeah. Math seems to work out. It might be "a leak," or it might actually shred like an orange peel on the way down, but the result is the same. The resulting ball of rubber wouldn't be massive enough to hold onto any meaningful atmosphere. Now, one thing I'm not considering here is the air pressure itself - the air is moving outward, not inward, but I don't think it would be enough to take substantial chunks of the rubber with it. The rubber has 100 times the mass.
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Re: What-If 0046: "Bowling Ball"

Postby ijuin » Thu May 23, 2013 4:46 am UTC

snowyowl wrote:
Copper Bezel wrote:Edit: Disperse, apparently. A fun calculation with a slightly unsatisfying answer.

What if we tried more power?

A ball of air the size and density of the Sun would form... well, the Sun. The fact that it's formed of oxygen and nitrogen rather than hydrogen would be a bit odd, but stars can burn oxygen for a while.


To fuse nitrogen and oxygen takes a star close to the Chandrasekhar Limit in mass (1.4 solar masses), since a temperature of around 1 billion Kelvin is required compared to the 10 million Kelvin for fusing hydrogen. If the ball were filled with water vapor at the same density, it could fuse the hydrogen, though.

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Re: What-If 0046: "Bowling Ball"

Postby OP Tipping » Sun May 26, 2013 11:07 pm UTC

If an upscaled bowling ball were to suddenly come into existence, then there would be a period of compression as the materials become denser due to pressure. There would be chemical changes under such high pressures, as higher density compounds become more energetically favourable. Both of these would generate heat, and I'm sorry to say that Randall hasn't covered these aspects.
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Re: What-If 0046: "Bowling Ball"

Postby Red Hal » Mon May 27, 2013 1:20 pm UTC

Tangentially related, the roundest thing ever made - if scaled up to the size of the earth - would be extremely smooth. The largest ripple would be around 15mm, and the difference between the largest and smallest diameter would be less than 5 metres:http://www.newscientist.com/article/dn14229-roundest-objects-in-the-world-created.html
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