gravitational force act in pairs, and they act toward the center of the earth. does it mean that if u find yourself at the earth center will your fill weightless?
Welcome to PF; I'm not sure what you mean by "gravitational force act in pairs" so I'll go right to your question ... In the center of the Earth, there is no mass "below" you - so no net gravitational force acts on you from the Earth - though you will have your own gravity - so you could describe this as "weightless".
"does it mean that if u find yourself at the earth center will your fill weightless?" Yes, of course. (Assuming the Earth had perfectly spherical simmetry, otherwise its geometrical centre doesn't correspond to its centre of mass)
Continuing on with this question on weightlessness ... Suppose there was a spherical Void in the center of a Earth (assume equal density throughout) and the void was a vacuum similar to deep space. If a person with an astronaut suit was "floating" in this void, would the sensation be the same as that in deep space?
Yes, all locations inside a hollow symmetric spherical shell of constant thickness and density provide a net gravitational acceleration of zero. This is true for a sphere of any size, a symmetric shell of any thickness of constant density, any size hollow symmetric centered space within the shell, for any location within the hollow space within the shell, not just the center. The inverse square relation and the distance to the way the mass is distributed in the shell makes this so for all locations inside the shell. Also, gravitation is an acceleration, not a force...
What do you mean by this? Gravity is most certainly a force in the Newtonian framework. Don't confuse the force of gravity with the strength of the gravitational field, the latter of which is an acceleration.
@iluvtek: welcome to PF; You can quickly understand the answer to your question by figuring out where the sensation of "being in deep space" comes from.
Although I understand zero gravity does not exist, let's assume deep space is located in area virtually free of any gravitational pull. Wouldn't this be different than having a uniform gravitation force applied from all directions (as is the case with the void in the earth)? If the gravitation pull was strong enough wouldn't this create a type of tensile stress on the astronaut's body?
The void (in the Earth or shell) has no gravitational gradient (no tidal effects), the space there is flat at all interior locations... same as "zero gravity" deep space.
No stress would be present, as there is no gravity gradient inside a hollow shell. It is 0 at all points. It's counterintuitive, but it is how the math works out!