gravitcal forces inside a hollow space body

n3mss said:
Just forget about inwards/outwards for a second. All bodies with mass "attract" each other (gravity). There is no "outwards", just "inwards"; bodies with mass do not repel each other like magnets with the same polarity. So, at the centre of a circle (yep, forget about the sphere for a moment) the question is "for the body at the centre of circle, how much gravity is exerted upon it by each point on the circle?" It doesn't matter what the actual number is... the point is that each point on the circle "exerts" the same gravitational pull as every other point on the circle (although with different vectors). The nett effect is that 0 force is exerted on the thing in the middle of the circle (all the numbers cancel each other out).
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But you would be pulled apart if you weren't strong enough and the force was high enough (if you were a single point at the exact centre then the above is true?)

Also if you moved off centre you would be pulled to the side of the hollow? (again assuming force were massive
 
It would be impossible for you to be at the centre of it because you would have to be infinitely small to be in the centre of a perfect sphere. Say you were infinitely small and that you could survive anything would you be held in suspension but if you tried to move you would get violently thrusted back into the middle as if by a spring.

Everything I said is probably untrue.
 
Zero gravity.

You can prove it easily enough by solving Laplace's equation in spherical co-ordinates. Most second year undergrads in physics / maths / engineering will have done this - it's a fairly well-known example.

Conceptually, however, you can see that there must be near-zero gravity: If you're sitting at the centre of the sphere, then you are being pulled equally in all directions: The amount of mass above you is equal to the mass below you, so the force pulling you "up" is equal to the force pulling you "down", resulting in a net gravitational force of zero. For a spherical body this is true whichever way you orient yourself, and so the net force at the centre will be zero.


Another well known, related result: If you were to "dig a tunnel" through the centre of the earth, through to the other side, and jump in, then you would exhibit damped oscillations about the centre - the damping being due to air resistance.



Edit: Goddamnit, I've got to start looking at who starts the thread before replying. Trolled again - yay Kwerk :rolleyes:
 
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Ghosteh said:
However, if you were to drift towards one side, you'd get pulled towards that side until you were at the edge.
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al4x said:
Also if you moved off centre you would be pulled to the side of the hollow? (again assuming force were massive
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No - net force will always be towards the centre of mass pulling you to the centre of the room.

Mason- said:
Say you were infinitely small and that you could survive anything would you be held in suspension but if you tried to move you would get violently thrusted back into the middle as if by a spring.
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Assuming this moon is moon/planet size and the room is room sized it would not be violent at all. Net gravitational force would be 0 at the centre of the room and pretty damn close to 0 at the edges of the room.
 
Duff-Man said:
True, though you need an additional assumption of a near-frictionless surface coating on the "tunnel". By drilling through the centre you have no force component pushing you towards the sides...
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iirc it's calculated that it takes ~42 minutes no matter where the two points th straight tunnel comes out are.
 
GravityPlot.png

(The Earth's radius is around 6.3 x 10^6 m, so actually I think the units on this pic should be 10^6m).
 
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edscdk said:
taken to the extreme and you are in the centre of a neutron star in a room, would you be ok or torn apart?
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Well, with the amount of gravity, if you were able to create a spherical room in the centre of a neutron star, and you were in it, I think you'd essentially be crushed as you'd have extremely high gravity on you at all sides.
 
Ghosteh said:
Liampope said:
No - net force will always be towards the centre of mass pulling you to the centre of the room.
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Oh yeah, of course. For some reason I was thinking about that backwards. I'll blame the lack of sleep, and the fact I'm back on a 24 hour duty!

Well, with the amount of gravity, if you were able to create a spherical room in the centre of a neutron star, and you were in it, I think you'd essentially be crushed as you'd have extremely high gravity on you at all sides.
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Perhaps I'm misunderstanding what you guys are saying. There will be zero net force anywhere inside the spherical shell - that's the point. It's obvious there will be zero net force at the centre of the shell, what's less obvious is that there is no net force everywhere inside the shell.

For those with a mathematical background, this is a direct consequence of the following facts:

1) Gravitational potential is harmonic on interior of shell.
2) By symmetry must be constant on surface of shell.
3) Weak maximum principle.

Newton's proof is more involved, but uses very basic (by today's standards!) mathematics.
 
Liampope said:
No - net force will always be towards the centre of mass pulling you to the centre of the room.



Assuming this moon is moon/planet size and the room is room sized it would not be violent at all. Net gravitational force would be 0 at the centre of the room and pretty damn close to 0 at the edges of the room.
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But the centre of mass isn't in the middle surely?
 
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