Does Gravity Pull Outwards on Objects Within Hollow Spheres?

[rubeszilla]

Hi all,

I have a question for the brainiacs. What would happen in this situation:

Imagine you have a ball, like a tennis ball, it has a skin and is empty inside. Now imagine the ball is immense and the skin, unlike a tennis ball, is much thicker than the space in the interior. This thick skin is immense and made up of solid matter. Now imagine there is a speck of minute dust floating in this interior.

Would that speck of dust feel a gravitational pull from the skin and move outwards towards the skin?

Thanks.

 

[Yuqing]

Newton's shell theorem suggests that the space within a spherical shell mass wouldn't feel any gravitation attraction at all.

http://en.wikipedia.org/wiki/Shell_theorem

 

[rubeszilla]

Thanks for that.

According to Newton, not. I wonder if there are any other opposing theories. Particularily if you consider the shell consisitng of phenomenonly greater and denser mass.

 

[sophiecentaur]

Density and mass are irrelevant; the Maths says Zero.
But, of course, we are dealing here with a perfectly symmetrical spherical shell. That is never the case, in practice, so you would expect some vestigial forces on an object inside a real shell.

 

[rubeszilla]

So assume the shell is egg shaped. What do you mean by vestigial forces? Numerous other forces but not a gravitational pull to the shell?

 

[Buckleymanor]

Density and mass are irrelevant; the Maths says Zero.
But, of course, we are dealing here with a perfectly symmetrical spherical shell. That is never the case, in practice, so you would expect some vestigial forces on an object inside a real shell.

You can have an eliptical or rugby ball shaped shell and the gravity inside is still zero.

 

[sophiecentaur]

I have a feeling that you're wrong about that. At least, the simple proof fails for anything other than a sphere - except right at the centre. The force is zero anywhere inside a spherical shell.

 

[DaveC426913]

So assume the shell is egg shaped. What do you mean by vestigial forces? Numerous other forces but not a gravitational pull to the shell?

By vestigial forces, he means: if the shell is not perfectly spherical and uniformly thick, then there would be some imbalances.

This is certianly true with non-uniform thickness of the shell; the jury seems to be out on whether it is true for non-spherical shape of the shell. I have yet to find a reference that addresses it.

 

[rcgldr]

In another thread, it was suggested that gravity from an infinitely long hollow cylinder would tend to pull objects to the wall of the hollow cylinder. I'm not sure if this was settled though.

 

[rubeszilla]

Ok. Well I've been thinking about the anomalies in gravity, particularly "accelerating expansion" where the metric expansion of space seems to be speeding up. Dark energy is used to explain this but I thought, what if the universe was encased in dense matter, perhaps an ellipsoid or egg shape and could that explain the pull.

Yes, it's a rather far out (excuse the pun) proposition, but seeing we have no idea what's at the edge of space it might be something to ponder...

 

[Buckleymanor]

By vestigial forces, he means: if the shell is not perfectly spherical and uniformly thick, then there would be some imbalances.

This is certianly true with non-uniform thickness of the shell; the jury seems to be out on whether it is true for non-spherical shape of the shell. I have yet to find a reference that addresses it.

Try this.http://brd4.braude.ac.il/~karp/Calgary.pdf

 

[DaveC426913]

Try this.http://brd4.braude.ac.il/~karp/Calgary.pdf

Well that's beyond my ken, but it seems to be saying that 'no gravity in the cavity' applies to ellipsoids as well.

I find it hard to believe. I think a high eccentricity ellipsoid (major axis is much longer than minor axis) should make it obvious.

 

[sophiecentaur]

I find it hard to believe too.
And stop calling me Ken

 

[Antiphon]

I find it hard to believe too.
And stop calling me Ken

Your instinct is correct. In general it would not be zero, however you can always place a nonuniform mass distribution around the periphery of a rugby ball or any arbitrary shape so that it would be zero inside.

To see how, simply solve the electrostatic problem of charge distribution on an arbitrary metal shape. The equilibrium charge distribution is the one that produces zero field inside. The Newtonian case is the same except for an opposite sign on the potential.

I don't know if this can be done in GR for high curvature fields.

 

[Buckleymanor]

Well that's beyond my ken, but it seems to be saying that 'no gravity in the cavity' applies to ellipsoids as well.

I find it hard to believe. I think a high eccentricity ellipsoid (major axis is much longer than minor axis) should make it obvious.

By that I take it that you agree that there is no gravity in the cavity.The minor axis being broken up into a series of concentric rings or a section through a sphere.While movement along the major axis just puts more wall one side or the other the net result being the gravitational force balenced.

 

[DaveC426913]

By that I take it that you agree that there is no gravity in the cavity.The minor axis being broken up into a series of concentric rings or a section through a sphere.While movement along the major axis just puts more wall one side or the other the net result being the gravitational force balenced.

No. I surmise that it does not work for ellipsoid shells, but I can't prove it.

 

[Disinterred]

Maybe a gravitational form of Gauss's Law for Electrical fields would quickly solve the problem of whether ellipsoidal shapes with hollow interiors have a gravitational field inside.

Then again, I have no idea.