Determining the Mass of the Earth

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rwald
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Post by rwald » Tue Jun 22, 2004 12:51 am

No, no, here's how you do it. You set up lasers on all the other planets, with observers manning each one, and use the scale as a mirror to direct these lasers to other planets. And then apply some gigantic mess of equations which use the known masses of the other planets and the calculated properties of Earth's orbit to determine Earth's mass.
For the record, I don't actually know anything. Not even this.

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Post by Skeptoid » Tue Jun 22, 2004 1:27 am

Pretend the Earth is ice cream and eat it. Take the scale to the Moon and weigh yourself. Since the Moon has 1/6 of the Earth's gravity, you just need to solve this easy equation to find the Earth's mass:

1/6 x (You + Earth) = Weight on the moon.

Therefore, E = 6W - Y.

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Post by Cool Hand » Tue Jun 22, 2004 1:18 pm

Skeptoid wrote:Pretend the Earth is ice cream and eat it. Take the scale to the Moon and weigh yourself. Since the Moon has 1/6 of the Earth's gravity, you just need to solve this easy equation to find the Earth's mass:

1/6 x (You + Earth) = Weight on the moon.

Therefore, E = 6W - Y.
I think after doing that you would need an awfully big Tums. You might want to call ahead first and see if they make one that big.

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Post by Cool Hand » Tue Jun 22, 2004 1:19 pm

rwald wrote:No, no, here's how you do it. You set up lasers on all the other planets, with observers manning each one, and use the scale as a mirror to direct these lasers to other planets. And then apply some gigantic mess of equations which use the known masses of the other planets and the calculated properties of Earth's orbit to determine Earth's mass.
This one is acceptable only if the lasers are on the heads of freaking sharks.

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And you run and you run to catch up with the sun but it's sinking
Racing around to come up behind you again
The sun is the same in a relative way, but you're older
Shorter of breath and one day closer to death.

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Post by hammegk » Tue Jun 22, 2004 2:13 pm

Let's throw the scale & the red herring out the window.

Anyone got a good timepiece? :P
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Post by Cool Hand » Tue Jun 22, 2004 2:35 pm

hammegk wrote:Let's throw the scale & the red herring out the window.

Anyone got a good timepiece? :P
I used to have a Timex when I was a kid. You could throw it out the window and it would still be ticking after that licking.

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Post by xouper » Sun Jun 27, 2004 10:34 am

Cool Hand wrote:
Abdul Alhazred wrote:Wait wait, I've got it.
Drop the scale from a known height and measure
how long it takes to hit the ground.
There ought to be enough information in that to
calculate the mass of the earth.
Yep. That's it. Of course you also have to know the radius of the Earth. We know it's approximately 6,371 kilometers, on average.
Caveat - do not drop it from such a great height that aerodynamic drag or tort law becomes a factor. For example, do not drop it from the top of the Sears Tower in Chicago.

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Post by Abdul Alhazred » Sun Jun 27, 2004 5:51 pm

xouper wrote: Caveat - do not drop it from such a great height that aerodynamic drag or tort law becomes a factor. For example, do not drop it from the top of the Sears Tower in Chicago.
I was picturing picking up the scale and dropping it from the height of my head, which can be easily measured before the experiment.
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Post by rwald » Sun Jun 27, 2004 11:00 pm

xouper wrote:
Cool Hand wrote:Yep. That's it. Of course you also have to know the radius of the Earth. We know it's approximately 6,371 kilometers, on average.
Caveat - do not drop it from such a great height that aerodynamic drag or tort law becomes a factor. For example, do not drop it from the top of the Sears Tower in Chicago.
Tort law? What, are you worried about the scale being sued on the way down, or its passage being hindered by red tape?
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Post by hammegk » Mon Jun 28, 2004 1:12 am

Radius? Use the scale as pole. :P
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Post by Walter_Wayne » Mon Jun 28, 2004 1:14 am

xouper wrote:
Cool Hand wrote:
Abdul Alhazred wrote:Wait wait, I've got it.
Drop the scale from a known height and measure
how long it takes to hit the ground.
There ought to be enough information in that to
calculate the mass of the earth.
Yep. That's it. Of course you also have to know the radius of the Earth. We know it's approximately 6,371 kilometers, on average.
Caveat - do not drop it from such a great height that aerodynamic drag or tort law becomes a factor. For example, do not drop it from the top of the Sears Tower in Chicago.
But if we put the Sears Tower in an evacuated bell jar we can calculate the coriolis effect ..., but we've been through that thread.

Walt

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Post by Sock » Thu Jul 08, 2004 2:57 pm

You would have to drop the bathrrom scale more than once. And from different heights. That would give you the Earth's gravitational acceleration.

And this still won't be enough information. Obviously, the greater the mass of an object, the greater sucking power it has (there is no gravity, the Earth sucks). But the farther you are from the center of the object, the less the acceleration (if I'm floating four light years from Earth, I'm not going to be pulled here in any great hurry). So mass is directly proportional, while distance is inversely proportional. And actually is it inversely proportional to the square of the distance.

Acceleration is in meters per second squared. So to get meters per second squared to equal a formula which has kilograms per square meter, you need another number. It will have to have cubic meters per kilograms seconds squared and be multiplied times the kilograms/meter to get it to all work out.

So you can't tell the mass of the earth with just a bathroom scale and knowledge of the diameter of the Earth. You have to know the gravitational constant as well.

edited to increase accuracy
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