I had a funny thought about gravity. Well, I suspect I know the answer, but am wondering. The gravity one feels toward an object depends on its mass and one's distance from the center of mass.

Now, suppose you have a very, very long, very, very thin wire in space, kind of like a space elevator, which is spinning like a propellor, so there is a center. Now, suppose it had a mass equivalent to the moon. If you were floating near the center of the wire (the place it's spinning around), would you feel an intense gravitational pull? Or would the gravity be distributed throughout the body?

__________________
As above, so below

Jens,

Actually, that's one of the standard static field problems one solves for both EM and (Newtonian) gravity. The electric and g-fields for a long wire will be the same, whether it's a wire of charge or mass.

For a long wire, near the wire (your distance to the wire is small compared to the length) the gravitational field is axial and inverse linear, directed radially toward the wire and it's strength depends on the density.

Far away, where your distance is very large compared to the length, it is inverse square and roughly GM/r^2, where M is the total mass. The near field morphs into the far field somewhere in between.

-Richard

I've no idea what Richards answer is... but mine would be as I think about it, it probably wouldn't matter much how long the wire or elevator shaft is if your spinning or floating in the center, it would depend on how fast you are rotating in the center or near the center I think. Centrifical force seems to add up quicker, just get on a merry-go-round and spin it, stand in the middle, then stand on the outside edge, then I think you'll get your answer. The more massive an object is, the harder it is that it would be to make it spin faster though, so I believe you wouldn't feel much in a long long long massive wire like elevator shaft that is spinning like a propeller and your in the very center. In fact I don't think you'd feel anything until you hit a wall and even then you'd fall or slide down toward the outside not feeling much of anything until you hit the bottom.

Funny...I interpreted the question different than both of you (I think). Here's my (non-expert) take on it.

If you were floating (stationary independent of wire movement) then...
If you were outside the spinning system, you would experience the normal mass at the center of gravity.
If you were insde a non-spinning system, then you would experience a portion of the gravity from one end of the wire, counteracted with the other end, and somehow including the distance you are from the wire. (I think this is what publius was saying but more mathematically)
If you were inside a spinning system, then the same would happen, but would be changing in direction. At the center, everything would balance at all times in all directions.

publius, doesn't your answer somewhat solve the gravitational anomolies noted in galactic rotation curves? By that I mean that due to the shape of the gravitating mass the field effects skew between a linear relationship and an inverse square relationship. Also the effects of gravity are different inside a "cloud" of mass (like a galaxy) than outside the cloud.

Those things are taken into account in the calculations.

Jens, your question has been answered by publius, but I think it is a common misunderstanding. The gravitational attraction of a body acts like a mass at its center of gravity if it is spherically symmetric. For other shapes, the formula is different, as publius explained in this case.

A good example is the Earth/moon system. Its center of mass, the barycenter, is only a quarter of the earth's radius under the surface, but we do not experience an attraction to that barycenter--it is more to the center of mass of the Earth (and even then, not exactly).

I figured as much but I had to ask the question/present the possibility.

and somebody should re-check, just to make sure...

hhEb09'1
Its center of mass, the barycenter, is only a quarter of the earth's radius under the surface, but we do not experience an attraction to that barycenter--it is more to the center of mass of the Earth (and even then, not exactly).

Is that because we are within the Roche limit, or the Hill Sphere? Not sure which applies, here.

No. It's an extreme example, but the general idea is, that the direction of the force is in general not to the center of mass.

It's true of spherically symmetric objects (of which there are very few), and it is a good approximation, especially when the distances between the objects are great.

OK, I'd like some clarification. You guys really hurt my brain this time.

I had offered the idea to a friend once that perhaps artificial gravity could be achieved by using a long, super dense band of material that ran the length of a spaceship. My thinking was that if the band were placed along the longitudinal axis of a cylindrical spaceship, then a person in the ship would feel a pull to this axis, no matter how far away from the ship's center of gravity s/he was, creating gravity that went 'in' (toward's the ship's center) instead of 'out' (like artificial gravity created by rotating).

However, I abandoned this idea because my friend and I eventually decided that the long, thin shape for a superdense material would be unstable and that it would try to collapse into a sphere. Now I find that there are different ways to consider it based on the shape involved.

Does the 'wire' have to spin? Can it remain still and maintain a stable configuration? How complex would the calculations be and what variables are involved? I'd like to play with it a little and explore the plausibility of an old idea. Any help would be greatly appreciated.

I pretty much suspected that, because I couldn't imagine that a long thread, even very massive, would pull you in when you approached the center. And thanks to publius for the answer that, while enlightening, I can't say I fully understood.

__________________
As above, so below

One thing to consider is the "gravity well" of the wire. When the wire was a sphere, prior to being extruded into a wire, there was a definite gravity well that the mass of the sphere produced but as the wire is extruded the well is destroyed just as the gravity well of a star is destroyed when it explodes into a supernova.

From an infinite distance the sphere and the wire have the same gravitational effect but as you decrease your distance a distinction begins to become evident: the sphere appears the same, gravitationally, from any direction whereas the wire appears to be gravitationally different from every vantage point.