Science Questions

Why is gravity weaker at the centre of the Earth?

Thu, 25th Oct 2012

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Question

Muhammad Al-Hakeem asked:

As we progress down to the very centre of the core of the Earth, why does gravity weakens while gravity should increase toward an object? And why does pressure take over?

 

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Muhammad al-Hakeem

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There is a similar discussion here.

http://www.thenakedscientists.com/forum/index.php?topic=45321

Due to the low density crust, the gravity doesn't change much as one tunnels through the crust.  It then decreases as one continues towards the center of the Earth.

Wikipedia has some discussions here.
Here's the discussion associated with the image.
http://en.wikipedia.org/wiki/Structure_of_the_Earth
http://en.wikipedia.org/wiki/Gravity_of_Earth

Consider that gravity has a direction towards the center of the earth, and a magnitude. 
However, once you arrive a the center, what direction is "down"?

As one would descend deeper into the core (which, of course, is very hot), one is not only attracted by the mass of the Earth below oneself, but is also attracted by the mass of the earth above oneself.  Thus, as one gets closer to equal parts of earth above and below oneself, the gravity decreases to nothing.

Pressure, of course, increases due to the cumulative effect of the weight of everything above oneself.  Consider in the ocean.  On the surface, we experience about 1 ATM of pressure due to the weight of the oxygen/nitrogen atmosphere.  As we descend, every 33 feet is equal to another ATM of pressure.  So, at 33 feet, we would experience 1 ATM of atmosphere pressure + 1 ATM of pressure from the weight of the water above oneself for a total of 2 ATM.  At 66 feet, another ATM of pressure, or 3 ATM total.  At 99 feet, another...  and etc.  CliffordK, Sat, 25th Aug 2012

Perhaps one could consider the gravity at the center of the Earth like standing at the North Pole.

Which direction is North from the North Pole?  Technically there is no North from the North Pole.
Which direction is South?  Going in any direction along the surface of the Earth is southward from the North Pole.

Likewise, at the center of the Earth, there is no "down", and all directions are "up".  And, thus, one would not experience gravitational pull. CliffordK, Sat, 25th Aug 2012

It is a common mistake to think that because the text books say that the surface gravity of an object is as if all the mass was concentrated at the "centre of gravity" of that object  i.e. the centre of a spherical object they fail to stress that the gravity falls off linearly to zero as you approach the centre of the sphere.

There are two other facts that it is useful to remember that the gravity in a uniform density medium of indefinite extent is zero because all the forces are equal in all directions.  Also the gravitational force inside a spherical cavity inside a uniformly dense medium of indefinite extent is zero everywhere inside the cavity.

This last rule also applies to a body with spherical symmetry as you move towards the centre.  it is only the total mass inside the spherical volume defined by your position with respect to the centre of the sphere that defines the force on you.  This falls to zero as you approach the centre Soul Surfer, Sat, 25th Aug 2012

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