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I have read that the Earth has a semi-solid iron body at its core, even though that object is surrounded by liquid magma.... I'm wondering if this is because of a pressure (and resulting temperature) differential -- or if there is another reason.

1) Since the forces of gravity of a sphere are at equilibrium at the center of the sphere -- doesn't that mean that the pressure at the mass center of a planet would be zero -- since there would be no "force" to be distributed at that area?

If the answer to #1 is true, then it leads to these further questions....

2) At what point between the surface and the center of the planet would the pressure be the greatest?

3) Would the depth in the Earth, at the max. pressure point specified in #2, be where we would expect to find the central layer of the Earth's magma? -- (Since pressure generates heat, wouldn't that be the hottest point; from a "pressure variable only" view?).

4) Shouldn't it actually be cooler at the Earth's mass center, than at the max. pressure point specified in #2 -- since the pressure is lower at the mass center?

4.a) And could that center temperature be enough cooler that it allows a core body to semi-solidify?

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1) Maximum pressure is in Earth's mass center. As, you say, all gravity forces cancel each other out at the center since the mass of Earth is symmetrically distributed around you. But the pressure in one point does not just pedpend on gravity in that point. Pressure is due to the weight of everything above you, and in those points, gravity is definitely not zero. Pressure is the integral of gravity (multiplied by mass density) from where you are all the way up into space. Hence, the pressure gradient is proportional to gravity and the fact that gravity is zero in the center of Earth is consistent with it being the pressure maximum.

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    $\begingroup$ And pressure is a scalar, so there is no issue of pressure coming "from all directions" either. $\endgroup$
    – gerrit
    Commented Jan 15, 2013 at 13:36
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This was exactly what I was thinking about, but I just realised what the problem is.

Gravity attraction does not stop at the earth core. We are failing to take into account that there's gravity consistently coming from the other half of the planet.

All gravity is essentially positive towards the centre, because any point 'halfway' between core and surface is being attracted by the other half of the planet as well as whatever distance is between it and the core. It can never achieve greater gravity in any direction other than the centre, because either you're at the centre, or the most of the planet mass is (even if just fractionally) in the direction of the centre.

Sorry if that's a little confusing. I kind of had to think through it on the spot, since I was trying to find out the answer as well. But that seems to be it.

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