Gravity at the center of the Earth?

mark,

Who was it that suggested the phrase "There gold in that astroid" was the solution to protect earth from impacts?

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Jeremy, You ask good questions and I'm glad you do so. The reason pressure rises is because mass per unit of area increases-right? So, in a sphere the mass tends to be greater near the surface-right? 50% of the mass of a sphere is in the outer 20% of its radius. The mass is the home of gravity force and since 50% of the mass is in the outer shell of the sphere 50% of the gravity force is also there. 50% of the gravity force is opposing the opposite 50% that is inside the sphere.(I hope this is not too confusing) So the max gravity is at the interface of the two spheres. Gravity being the force underlying pressure it follows that pressure is greatest somewhere near the interface of the two spheres and falls off as you go deeper to the mass center. Draw the two spheres and do the math and you aggree.
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Well I'm sorry Jim but I draw the two spheres and my math doesn't agree. You are forgetting that a plane drawn perpendicular to the radial line going from the core to your halfway point has significantly more mass below the plane than it does above it. You are forgetting all the mass on the other side of the Earth that is pulling also. This is a basic math problem performed since the time of Newton. The forces only equalize at the center of the sphere, at every other point there is a net pull towards the center. Think of it this way, imagine my perpendicular plane again. All mass units above the plane are pulling the object upward and all the units under it are pulling it the other way. All the points near the plane are equalized out and don't affect things much. The amount of mass pulling is always greater until you reach the center where the plane divides the Earth into equal amounts.

Jeromy, I aggree with most of what you got here. The mass of a sphere is mostly in the outer part of the radius because the volume grows in proportion to R^3. If you divide the sphere into two equal mass spheres; one hollow-one solid and separate the two spheres you will see a different result as to where the gravity attraction is.

You can divide the sphere in the manner you choose and it does not change the situation, you cannot declare the two masses separate when they are clearly one body. Moreover, your outer sphere is a hollow shell and has no net force inside it while your inner sphere does have a net force that points towards the center and you have pressure again. You have to sum ALL the masses acting on your particle not just the ones you want. If you take a perpendicular slice through the Earth it is clear to see that a majority of the mass lies BELOW where your halfway point is and it is going to win the battle in tug of war. I don't know how else I can put it to make myself clearer.

Any comment on my post pondering differing densities changing the mass distribution scenario? - MV

I'll take a stab at it

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I assert that the core could be compressed gases and actually have a higher density. Your mass distribution only holds if density is constant throughout. I imagine a structure where the mass of the solid and liquids above supercompresses a core of hydrogen gases. An example of this is Jupiter whose atmosphere is so dense that penetrance by even a solid is difficult. We know that jupiter is ~ 90% H2(g). Even with best research on Earth we are uncertain of even the state of matter let alone the composition of the mantle let alone the core. Maybe we shouldnt drill too far, might make a gas jet and crack the planet.
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I do know that someone named Owen proposed a plasma core for the Earth. All that we know about the interior is based on theory since we can't actually dig down there. Any gas core theory is going to have to show a mechanism whereby such a thing can happen, it will also have to deal with showing the proper velocity profiles of seismic waves. I think Herndon makes a good case for a nuclear core. Others have proposed compressed metallic hydrides or even ice layers. We just don't know for sure.