Gravity and point mass confusion

[fawk3s]

I think I am missing the point of center of mass here but help me understand.

So we calculate the gravitational acceleration on Earth with the Newton's law of gravitation equation, but what gets me confused is the fact that we look at Earth as a point mass. As Earth is "big and round", I don't really understand how do these forces act in order to give us the same number in the real case as it would be in the point mass case (looking at Earth as point mass).

For example, if we sliced a thin layer out of Earth and observed it:
http://img684.imageshack.us/img684/324/earthmass.png

Wouldnt the point-mass case have more force acting on the person than the real case? Because the edges are further away from the person?
I mean, wouldn't there be more force acting on the person if we observed the thin layer as point mass?

Thanks in advance

 

[Doc Al]

The fact that a spherically symmetric mass distribution (a shell or solid sphere) exerts the same gravitational force (for points outside its radius) as if its mass were concentrated at its center is a special result first proven by Newton himself. It's not obvious! Look up Newton's Shell Theorems.