Does Gravity Pull Outwards on Objects Within Hollow Spheres?

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Discussion Overview

The discussion revolves around the gravitational effects experienced by an object within a hollow spherical shell, particularly focusing on whether such an object would feel a gravitational pull towards the shell. Participants explore theoretical implications, including variations in shell shape and density, and consider related concepts such as gravitational anomalies and the nature of gravitational fields in non-spherical geometries.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants reference Newton's shell theorem, which suggests that an object inside a perfectly symmetrical spherical shell would not experience any gravitational attraction.
  • Others propose that if the shell is not perfectly symmetrical or uniformly thick, there could be vestigial forces acting on an object inside, although the nature of these forces remains debated.
  • A participant raises the idea that gravitational effects might differ for non-spherical shapes, such as ellipsoids, and questions whether gravity would still be zero inside such shells.
  • There is mention of gravitational behavior in other geometries, such as hollow cylinders, which may influence the discussion on hollow spheres.
  • Some participants express skepticism about the applicability of the shell theorem to non-spherical shapes, suggesting that gravitational forces may not be zero in those cases.
  • One participant speculates on the implications of dense matter surrounding the universe and its potential effects on gravitational behavior, linking it to concepts like dark energy.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether gravitational forces exist within non-spherical shells, and multiple competing views remain regarding the effects of shell shape and density on gravitational attraction.

Contextual Notes

Discussions include references to mathematical proofs and theoretical frameworks, but limitations exist regarding the application of these concepts to non-uniform or non-spherical mass distributions. Some assumptions about symmetry and uniformity are not universally accepted.

Who May Find This Useful

This discussion may be of interest to those exploring gravitational theory, particularly in relation to shell structures, non-standard geometries, and the implications of gravitational anomalies in cosmology.

rubeszilla
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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.
 
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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.
 
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.
 
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?
 
sophiecentaur said:
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.
 
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.
 
rubeszilla said:
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.
 
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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.
 
  • #10
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...
 
  • #11
DaveC426913 said:
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
 
  • #12
Buckleymanor said:

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.
 
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  • #13
I find it hard to believe too.
And stop calling me Ken :smile:
 
  • #14
sophiecentaur said:
I find it hard to believe too.
And stop calling me Ken :smile:

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.
 
  • #15
DaveC426913 said:
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.
 
  • #16
Buckleymanor said:
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.
 
  • #17
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.
 

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