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Author Topic: Where do we feel the Earth's gravitational pull the strongest?  (Read 30758 times)

@TaySharpe

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@TaySharpe asked the Naked Scientists:
   
If Earth's gravity is weaker as you move to the centre, where will you feel the strongest measure of gravitational pull?

What do you think?
« Last Edit: 05/12/2010 19:30:04 by _system »


 

Offline Geezer

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Ah! Good question.

Assuming we assume the Earth is spherical (which it really isn't), and that it has uniform density throughout (which it doesn't), I'm guessing the greatest attraction will be at the Earth's surface. However, as I have neglected to do any of the tedious calculus that is necessary to form this conclusion, I would not be surprised to learn that I am wrong.
 

Offline Bored chemist

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"Assuming we assume the Earth is spherical (which it really isn't), and that it has uniform density throughout (which it doesn't), I'm guessing the greatest attraction will be at the Earth's surface."
Which is wherever we are, which isn't very helpful.
The Earth is a bit squashed in at the poles so they are slightly nearer to the centre so gravity is slightly stronger there.
Also the rotation of the Earth tends to throw things off at the equator, weakening gravity's apparent effect.
The place where you are easiest to lift up is the equator.
However, if you can find a tall mountain near the equator that might be even better.
The place where gravity is at it's biggest must be the North or South pole- I think the South has bigger mountains so I'd go North.

Personally the place I feel it most is trying to get out of bed.
 

Offline Geezer

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Ah! I took the question to be something like - "What happens if you dig a hole in the Earth. Will gravity diminish as you descend into the Earth?" Isn't that what "move to the center" would mean?
 

Offline CliffordK

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Wikipedia has a wonderful Grace Project Geoid Representation of Earth's gravity.

http://en.wikipedia.org/wiki/Gravity_of_Earth




So the Andes and Himalayas and other mountain chains show up as some of the highest gravity points on the Geoid representation by the Grace project (see note below).

They also have this file...
Showing the gravity is greatest at about 2885 km below the surface.
Unfortunately, there is little explanation about it, or the calculations to derive that information.  Notes I saw on the WWW indicated that Earth's core does not have a constant density which could confound many simple calculations.



There is an article:

Gravitational field strength inside the Earth
Laurent Hodges
American Journal of Physics -- October 1991 -- Volume 59, Issue 10, pp. 954-

No abstract...  and one must pay excessive amounts to download, but it looked like it could be interesting.

Actually, thinking about this, there may be a fallacy with the Grace project (first image).
Earth's gravity as measured from space may not be the same as Earth's gravity as measured from the surface.
I'll let you ponder that for a bit... then hopefully I'll chime in and give my explanation
 

Offline CliffordK

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Ahhh...
Reading the Wikipedia links...  this is a clearly written document & makes some sense...

http://www.chsfootball.net/earth_g_2.doc

Like the image above...  it says the peak gravity is about 10.7 m/ at the core-mantle boundary due to the density of the earth.

Also...  Due to the bulge in the earth and centrifugal/centripetal force, the gravity is greater at the poles 9.832 m/ than the equator 9.780 m/

See my note above about the potential fallacy about the gravity as measured from Space by the Grace Project.
 

Offline maffsolo

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Not trusting a non certified EDU site I focused my sight on a science formula that has an explanation.
In doing so, applying a mathmatical rule of thumb and a mathmaticians rule. At least this time,

F=(GMm)/R2=mg

Where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and R is the distance between the of the two objects (in this case, the distance is between you and the center of the Earth.)

Therefore it could be assumed that the closer you are to the center of the Earth (the lower the elevation), the stronger the force of gravity.

If I remember correctly the lowest place in the U.S. is Death Valley at -282 ft (-85.9536m). Given that the mean radius of the Earth is 6.37*106m, we could calculate g, acceleration due to gravity, in Death Valley using the equation above:

g=((6.673*10-11)(5.98*1024))/(6.37*106-85.9536)2 =9.834565215 m/s2
Where
G=6.673*10-11

M=5.98*10+24
Compare this to the gravitational field calculated using the mean radius: 9.834299811 m/s2
As you can see, the difference is so small, it is insignificant.
http://www.physlink.com/education/askexperts/ae375.cfm
=======================

According to the formula, digging a hole to the center of the earth M and m is constant. 
F will increase indirectly porportional to the radius of distance to the center.
Then, at the center, the radius becomes so small approaching zero, by La H'opitals rule F approaches infinity? Not zero as suggested.
I should say little g instead of big F since little m cancels out.
« Last Edit: 11/12/2010 13:35:09 by maffsolo »
 

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