## Determining the Mass of the Earth

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rwald
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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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Skeptoid
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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.

Cool Hand
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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.

Cool Hand
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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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Cool Hand
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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.

Cool Hand
....life purpose is pay taxes -- pillory 12/05/13

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.

"Time" -- Pink Floyd

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

Anyone got a good timepiece?
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Cool Hand
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hammegk wrote:Let's throw the scale & the red herring out the window.

Anyone got a good timepiece?
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.

Cool Hand
....life purpose is pay taxes -- pillory 12/05/13

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.

"Time" -- Pink Floyd

xouper
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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.

Abdul Alhazred
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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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rwald
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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?
For the record, I don't actually know anything. Not even this.

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hammegk
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Title: Curmudgeon
Location: Hither, sometimes Yon
Radius? Use the scale as pole.
The most important things in life–beauty, grace, redemption, compassion, loyalty, love–are beyond the reach of reason. Which doesn’t make them any less real. Stay far back: I'm allergic to Stupid.

The simple rule, the greatest plan, that he should keep who has the power, and he should take who can.

The only enemies of guns: rust ... and politicians.

Philanthropist (n.) - Someone who spends his own money to advance his version of Utopia. Socialist (n.) - Someone who spends your money to advance his version of Utopia.

“Jesus loves the little cheeses, all the cheeses of the world. Swiss and Cheddar, stinky, too. If He loved them, so should you. Jesus loves the little cheeses of the world.”

I'm right 98% of the time; who cares about the other 3%?

Walter_Wayne
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Location: Ottawa
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

Sock
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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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