What-If 0085: "Rocket Golf"

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Various Varieties
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Re: What-If 0085: "Rocket Golf"

Postby Various Varieties » Tue Mar 04, 2014 12:41 pm UTC

Randall didn't completely answer the question!

The question asks: "How many golf balls would be required to reach the Moon?"

But he only replied with the size of our ball supply, completely missing out the quantity!

I for one am appalled by this glaring omission. :x

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Re: What-If 0085: "Rocket Golf"

Postby CasualSax » Tue Mar 04, 2014 2:22 pm UTC

Various Varieties wrote:Randall didn't completely answer the question!

The question asks: "How many golf balls would be required to reach the Moon?"

But he only replied with the size of our ball supply, completely missing out the quantity!

I for one am appalled by this glaring omission. :x


Volume of a sphere is: v= 4/3 * pi * r^3

Radius of the "final" bag of golf balls is 75 miles (4,752,000 inches), radius of a golf ball is ~ .85 inches.

Volume of the total of golf balls is 449487796497116448446.60456995839. Volume of an individual golf ball is 2.5724407845144423634278278236754.

Assuming all of that is right, that leaves us with about 174,732,028,508,854,060,655 golf balls.

"Yeah, I've been known to hit one hundred quintillion or two golfballs in my life."

"I'll guess the latter."

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Re: What-If 0085: "Rocket Golf"

Postby rmsgrey » Tue Mar 04, 2014 3:49 pm UTC

CasualSax wrote:
Various Varieties wrote:Randall didn't completely answer the question!

The question asks: "How many golf balls would be required to reach the Moon?"

But he only replied with the size of our ball supply, completely missing out the quantity!

I for one am appalled by this glaring omission. :x


Volume of a sphere is: v= 4/3 * pi * r^3

Radius of the "final" bag of golf balls is 75 miles (4,752,000 inches), radius of a golf ball is ~ .85 inches.

Volume of the total of golf balls is 449487796497116448446.60456995839. Volume of an individual golf ball is 2.5724407845144423634278278236754.

Assuming all of that is right, that leaves us with about 174,732,028,508,854,060,655 golf balls.

"Yeah, I've been known to hit one hundred quintillion or two golfballs in my life."

"I'll guess the latter."

Are you taking account of the packing fraction? Golf balls don't tessellate very well...

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Re: What-If 0085: "Rocket Golf"

Postby CasualSax » Tue Mar 04, 2014 7:47 pm UTC

rmsgrey wrote:
CasualSax wrote:
Various Varieties wrote:Randall didn't completely answer the question!

The question asks: "How many golf balls would be required to reach the Moon?"

But he only replied with the size of our ball supply, completely missing out the quantity!

I for one am appalled by this glaring omission. :x


Volume of a sphere is: v= 4/3 * pi * r^3

Radius of the "final" bag of golf balls is 75 miles (4,752,000 inches), radius of a golf ball is ~ .85 inches.

Volume of the total of golf balls is 449487796497116448446.60456995839. Volume of an individual golf ball is 2.5724407845144423634278278236754.

Assuming all of that is right, that leaves us with about 174,732,028,508,854,060,655 golf balls.

"Yeah, I've been known to hit one hundred quintillion or two golfballs in my life."

"I'll guess the latter."

Are you taking account of the packing fraction? Golf balls don't tessellate very well...


I did not, but I assumed that Mr. Monroe did not either, so the volumes would translate to the same number of golf balls (even though the volume is wrong).

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Re: What-If 0085: "Rocket Golf"

Postby NOTNOTJON » Tue Mar 04, 2014 8:00 pm UTC

Randall's last line
over the course of this maneuver you would be statistically likely to hit a hole-in-one ... at every golf course in the world.


Umm, no you wouldn't... 1000000+ tries to hit a golf ball into a hole and then finally getting a shot in doesn't equal a hole in one. It sounds more like my life at golf.

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Re: What-If 0085: "Rocket Golf"

Postby gmalivuk » Tue Mar 04, 2014 8:24 pm UTC

CasualSax wrote:
rmsgrey wrote:Are you taking account of the packing fraction? Golf balls don't tessellate very well...
I did not, but I assumed that Mr. Monroe did not either
Yes, he did. That's what the 65% number is here:
Image

Stripping that equation down to just the mass part, we get 1.616x1045kg for the initial number, which is 3.519x1046 1.62 oz regulation-sized golf balls.

For the final number, where each ball is going 140m/s, we get 5.523x1018kg or 1.203x1020 balls.

(The number of digits you gave, CasualSax, is incidentally pretty absurd, considering you estimated a single ball to only 2 significant figures. Those extra digits don't give any usable information, they just make it harder to see at a glance how big the numbers are.)

NOTNOTJON wrote:Randall's last line
over the course of this maneuver you would be statistically likely to hit a hole-in-one ... at every golf course in the world.
Umm, no you wouldn't... 1000000+ tries to hit a golf ball into a hole and then finally getting a shot in doesn't equal a hole in one.
It's not that many tries to hit a ball, though. It's one try for each ball.
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Re: What-If 0085: "Rocket Golf"

Postby CasualSax » Tue Mar 04, 2014 10:39 pm UTC

gmalivuk wrote:
CasualSax wrote:
rmsgrey wrote:Are you taking account of the packing fraction? Golf balls don't tessellate very well...
I did not, but I assumed that Mr. Monroe did not either
Yes, he did. That's what the 65% number is here:
Image

Stripping that equation down to just the mass part, we get 1.616x1045kg for the initial number, which is 3.519x1046 1.62 oz regulation-sized golf balls.

For the final number, where each ball is going 140m/s, we get 5.523x1018kg or 1.203x1020 balls.

(The number of digits you gave, CasualSax, is incidentally pretty absurd, considering you estimated a single ball to only 2 significant figures. Those extra digits don't give any usable information, they just make it harder to see at a glance how big the numbers are.)

NOTNOTJON wrote:Randall's last line
over the course of this maneuver you would be statistically likely to hit a hole-in-one ... at every golf course in the world.
Umm, no you wouldn't... 1000000+ tries to hit a golf ball into a hole and then finally getting a shot in doesn't equal a hole in one.
It's not that many tries to hit a ball, though. It's one try for each ball.


When we are doing napkin math for the sheer sake of absurdity, seeing the full number outright has more comical effect than scientific notation.

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Re: What-If 0085: "Rocket Golf"

Postby gmalivuk » Tue Mar 04, 2014 10:57 pm UTC

Ah, then I guess my mistake was doing math to answer the question asked...
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Re: What-If 0085: "Rocket Golf"

Postby Mikeski » Wed Mar 05, 2014 2:42 am UTC

NOTNOTJON wrote:Randall's last line
over the course of this maneuver you would be statistically likely to hit a hole-in-one ... at every golf course in the world.

Umm, no you wouldn't... 1000000+ tries to hit a golf ball into a hole and then finally getting a shot in doesn't equal a hole in one. It sounds more like my life at golf.

Since none of those balls were hit from the appropriate tee box (I know of no golf course with a green on earth and a tee box in orbit), none of them are holes in one. A million tries from the tee box would count if one of them went in. Though that's a truly Presidential number of rounds of golf, or a frighteningly permissive mulligan rule.

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Re: What-If 0085: "Rocket Golf"

Postby orbik » Wed Mar 05, 2014 4:09 pm UTC

flying_kiwi wrote:Olaf Klischat is correct -- for almost all configurations discussed, the escape velocity of the ship is greater than the launch velocity of the ball, so it will simply fall back to the surface of the ship after launch, and (assuming collisions are at least partially inelastic and it eventually comes to rest) the net change in momentum of the ship will be zero.

In the final configuration, plugging in the density of the average golf ball I get the launch velocity a little larger than the escape velocity, so the ship WILL move. However, the final velocity is still a good deal less than the launch velocity, which reduces the effectiveness of the rocket, forcing the designer to make it larger -- likely to the point you wouldn't be able to launch to escape velocity, and the rocket would fail to change its momentum.


I'm afraid it's even more complicated than that because the ship is a non-inertial reference frame. The launch speed doesn't need to exceed the ship's escape velocity because before the first ball drops back to the ship, it will have accelerated away from the ball. This is just based on intuition and I'd like to see someone more mathematically skilled actually write that out as an equation.

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Re: What-If 0085: "Rocket Golf"

Postby gmalivuk » Wed Mar 05, 2014 5:35 pm UTC

Yeah, but you could still consider it one ball at a time, to get a bound on it. If the launch speed is above the ship's escape velocity, shooting off the golf ball will definitely accelerate the ship. If it's equal or less, then the only way to accelerate is to fire off golfballs fast enough that your own velocity added to the ball's will exceed escape velocity (at a particular distance) before the ball stops.

Later I may actually do the math to find the speed at which it balances out exactly (i.e. where launch speed is equal to the full ship's escape velocity).

Edit: Now that it's later, I'll do the calculation. I'll furthermore do it with the more accurate 63.4% for random close packing and 1.13 kg/L for a golf ball.

If we set the initial equation equal to the radius for a given mass and escape velocity (where the mass is that given by the rocket equation), we need to find v so that
[;
\left(\frac{3}{4\pi}\exp\left(\frac{5300\ m/s}{v}\right)200\ kg \frac{1\ m^3}{.634*1130\ kg}\right)^{\frac{1}{3}}=\frac{2G\exp\left(\frac{5300\ m/s}{v}\right)200\ kg}{v^2}
;]
Then the velocity that works is a bit over 134m/s. Meaning that the last, fastest scenario in the what-if is the only one with any possibility of working at all, even if we ignore all the other matter in the universe.

Edit2: If we use the optimal 74% efficiency packing, the resulting speed is only about a third of a meter per second faster.
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Re: What-If 0085: "Rocket Golf"

Postby flying_kiwi » Sat Mar 08, 2014 10:28 am UTC

orbik wrote:
flying_kiwi wrote:Olaf Klischat is correct -- for almost all configurations discussed, the escape velocity of the ship is greater than the launch velocity of the ball, so it will simply fall back to the surface of the ship after launch, and (assuming collisions are at least partially inelastic and it eventually comes to rest) the net change in momentum of the ship will be zero.

In the final configuration, plugging in the density of the average golf ball I get the launch velocity a little larger than the escape velocity, so the ship WILL move. However, the final velocity is still a good deal less than the launch velocity, which reduces the effectiveness of the rocket, forcing the designer to make it larger -- likely to the point you wouldn't be able to launch to escape velocity, and the rocket would fail to change its momentum.


I'm afraid it's even more complicated than that because the ship is a non-inertial reference frame. The launch speed doesn't need to exceed the ship's escape velocity because before the first ball drops back to the ship, it will have accelerated away from the ball. This is just based on intuition and I'd like to see someone more mathematically skilled actually write that out as an equation.


I haven't worked it out, but it won't help much -- the ball loses most of its momentum immediately after the "launch", and it is during this time that the "equal and opposite" force on the ship will partially cancel out the impulse it gained from the initial launch.

Likewise, the gravitational acceleration on the ship and the ball from any external field will be initially identical (ignoring the finite size of the "ship"), and any difference will only become significant as they separate.


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