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In theory, you could have a (man-made) structure with NO core, a la the halos in the video game Halo or a empty sphere or something. In this situation if you were "inside" it, then yes, you would get pulled outward if the radius of the object was sufficiently large, the object had a whole lot of mass, and was separated from other significant gravitational fields.
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No, actually. If you are inside a spherical structure that is radially uniform, you feel no gravitational effects from it.
The calculus to show this was sort of fun. =)
To make it concrete:
Imagine you where inside a large, hollow, spherical shell. It is really really heavy.
Now, this shell 'pulls' at you.
If you are in the middle, in every direction there is the same amount of mass at the same distance. You feel no gravity.
Now, lets say you where nearer to one side.
Well, under the inverse square law, the gravitational force from that side is less attinuated by distance. However, there is
more stuff on the other side.
The two forces (the closer, smaller mass on your right, and the farther, heavier mass on the left) cancel each other out perfectly.
Another fun structure is the heavy hollow tube. Things inside the tube are pulled towards a plane that cuts the tube into two equal-sized tubes. I believe the strength of the pull goes up as you move further away from the plane, to a limited extent.
An interesting question: going back to the heavy, hollow shell -- is there any effects when accellerate and move from point to point?