Pickers said:dear oh dear - Gravity originates from mass, not the center point of a planet.
The misconception is a product of Newton's thereom, which proved that in a spherically symmetric distribution of matter, a particle feels no force from matter at greater radii, and the matter within the radii gives the same force as one would expect from a point source located at r=0. if you were at r = 0, assuming the earths matter distribution to be sherically symmetric, you would feel no contribution to gravity. Ergo, you would not be squashed, or pulled apart.
(of course, you would oscillate around this point if you had net motion to begin with)
I can't believe he waited to prove that spheres act like point masses before publishing!!! (at least thats what my teacher said)