Throwing Stuff Down A Mineshaft

subbie writes:

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I'm confused about whether there's no gravity at every point inside the sphere.

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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.

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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.

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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.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

cavediver responds to me:

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Relative to the shell, it doesn't matter what the external gravitational field is. The shell will respond to that field identically to the shell occupant, and again the occupant will be entirely weightless within the shell.

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But only with respect to the shell. I was trying to give an image of how the person could be floating within the shell.That is, assuming an empty universe except for the moon, you would be gravitationally pulled toward the surface of the moon if you were outside it.Inside it, however, you wouldn't be pulled toward any surface: You could float around inside it.If, however, you had both the moon as a spherical shell and there was the earth around it, you would feel the gravitational pull of the earth. If the moon is in freefall, then so are you within it and thus you don't feel anything.But if the moon were sitting on the earth, you would be standing on the shell were it was touching and would not be able to float to the top.That's why you don't float to the top of the house when you enter your home.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

cavediver responds to me:

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Obviously, in this case you are no longer simply inside a spherical shell, but a very lopsided mass distribution

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Not quite what you said, with

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Rrhain writes:

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Indeed, assuming that there is no other gravitational field anywhere else in the universe

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And if there were a gravitational field without the shell actually touching anything else, what then? No, not in free fall...the shell isn't moving, but there is a gravitational field in a certain direction external to the shell. That field would affect anything inside the shell.And people wonder why getting published is so hard. You have to submit your work to others to have them point out things you've overlooked (thank you, cavediver.) Edited by Rrhain, : No reason given.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

cavediver responds to me:

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Er, what do you mean by not "moving"? How is it not in free-fall? Does it now have engines strapped to the shell which are firing?

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I can think of a few ways to have the shell not moving. Perhaps the shell is magnetic and there is a magnetic force sufficient to counteract the gravitational pull. If there is something not affected by the magnetic field inside the shell, it would be standing on the edge of the shell closest to the gravitational field.Similarly, there could be some sort of fluid surrounding the shell providing buoyancy.The point I was trying to make is that under the influence of just the shell, a spherical shell's geometry provides perfect gravitational counterbalance in all directions internally. Perhaps I should have phrased it that way.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.