subbie writes:
quote:
I'm confused about whether there's no gravity at every point inside the sphere.
Indeed, assuming that there is no other gravitational field anywhere else in the universe, there is no gravitation pull inside a perfectly uniform, spherical shell.
quote:
Gravity operates according to the inverse square law, no? Therefore, it seems to me that if you are closer to one side than the other that the gravitational pull from the closer side would be stronger and, thus, draw you to that side.
Yes, but you need to take into account that as you get closer to one side of the sphere, you have a lot more mass behind you. Because the shell is spherical, it exactly balances out: The gravitational pull you feel in one direction is perfectly balanced by the gravitational pull in the opposite direction.
That is, suppose you have a shell with an internal diameter of 8000 km and a thickness of 1 km.
Suppose you are standing on a point on the inside of the shell. How much mass is "beneath" you? You can visualize a plane spreading out tangent to the point of contact that lops off a thin shaving of the sphere...kinda like what happens when they do LASIK on you.
But that means the entire mass of the rest of the sphere is "above" you and pulling in the opposite direction. Due to the geometry of the sphere, it just so happens that the gravitational pull of the small-but-close mass is exactly equal to the gravitational pull of the large-but-far mass.
This is true for all points inside the sphere: The pull on one side exactly counters the pull on the other.
Now, if you have a different shape such as a cube, then there will be gravitational field gradient inside.
Now, you could fake a gravitational pull by rotating the sphere. Along the equator in relation to the axis of rotation, you'll have the largest acceleration, diminishing to zero at the poles.
Rrhain
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