So I was in the shower today...

[Agamemnus]

The point you make is valid until you realise the average of all the atoms of Earth is it's (sic)center. And there, the gravitational attraction there is infinite.

If someone was to drill a giant hole directly through the planet that went directly over the center of mass, and you dropped a ball down the hole, it would (with SHM) modulate until it lost all it's energy, and 'hover' directly on the center of mass (obviously assuming it isn't affected by the rest of the universe).

.....

No.

Read the formula. . . .

If a particle was at the center of the Earth, the gravitational forces exerted on it would be 0. You're assuming the Earth is one whole "mass", but that's simply not the case. You don't put the Earth's distance from you into the equation if you're reasonably close to the earth. You must consider all the particles in the Earth or at least a subset of them.

Think about it. If you don't consider each particle in the formula then you can have weird outcomes that violate the law of conservation of mass and energy. For instance, infinite pull at the center. Now how does that make sense?


Rattrapmax6 is correct but I don't quite understand what he means by "slightly pulling outward"...
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EDIT:

thegrogen:

1) OK thanks..

2) Because the highest level of gravity would be located somewhere in between the center and outer core of the earth, where force-of-gravity "cancellations" are smaller. High levels of gravity means high pressure and that means a hot solid or perhaps a hot liquid.

3) Same as explanation to aetherfox. Even if pressure forced them closer together, you would still have little gravity in the center of the earth because of force cancellations.

4) ?????