If I created a bubble in the center of the Earth could I walk all around inside?

[Vortigon]

Hi all.

 

Before i ask my question I will explain my thought process so you can point out any errors.

 

I was thinking about the way that TV shows represent the gravitational effect of planetary bodies in space. Usually with a ball on a piece of fabric showing a curve in space-time. It suddenly occured to me that it was so simplified that it didnt satisfy my curiousity. I tried to visualise how this gravitational effect could be represented as it works in reality i.e. rather than just on a single plane that a piece of fabric represented, but how it would look on all degrees around a sphere. Really hard lol

 

So I moved on to wondering how small the the center of the gravitational field in the Earth is?... i.e. how big an area within the center of the Earth had an equal gravitational value, was it the size of a house or an atom. Then it dawned on me, there cannot be a single area at the center of Earths gravity, since as you got closer to the center of the Earth, the gravitational pull of the matter closer to the surface would eventually outway the pull of the material between you and the center?

Q: So finally my question is if I'm correct in my thinking, if I created an empty sphere in the center of the Earth of just the right size, could I walk all around inside the sphere, on it's inner surface, due to the gravitational effect of the remaining mass of the Earth outside of the imaginary sphere?

 

Sorry for the long winded post

[A Childs Mind]

My theroy is no. Because gravity would be so stroung the empty space would cave in.

[Vortigon]

Wouldn't it want to cave outwards or expand outwards?

[A Childs Mind]

so if thats was true. than it would constantly expand till every thing was pushed away from earth.

 

lol in reality in make another univers..... of nothing

[Sisyphus]

Then it dawned on me, there cannot be a single area at the center of Earths gravity, since as you got closer to the center of the Earth, the gravitational pull of the matter closer to the surface would eventually outway the pull of the material between you and the center?

 

This is incorrect. The gravitational pull is always towards the center. It does, however, get less and less the closer you get to the center. At the very center, there is no gravity. Think about how much stuff is on either side of you, at any given point.

 

Q: So finally my question is if I'm correct in my thinking, if I created an empty sphere in the center of the Earth of just the right size, could I walk all around inside the sphere, on it's inner surface, due to the gravitational effect of the remaining mass of the Earth outside of the imaginary sphere?

 

No. Inside a hollow sphere – any hollow sphere – the effect of gravity from the sphere is always zero. This can be shown mathematically, but it also makes intuitive sense, if you think about it. If you’re right next to the inside edge of this sphere, you’re obviously closer to that edge and would expect gravity to be pulling you that way, right? Wrong. While it is true that that portion of the sphere is pulling you the strongest, most of the sphere is pulling you in the opposite direction, and it cancels out.

[mooeypoo]

If you created a bubble in the center of the earth, (that has no matter in it, obviously), then you would theoretically have the same amount of mass all around you, and the forces of gravity will cancel out - you would, essentially, float.

[Vortigon]

Ahhh of course.. I can't believe I didn't think of that.

 

Thanks alot!

[swansont]

The other implication of all of this is that when you are outside of the earth, it behaves like all of the mass is at the center. Both situations assume the mass is distributed uniformly.

 

Both of these circumstances make it easier to solve certain gravitational and electrostatics problems (it's an artifact of the 1/r^2 force)

[Vortigon]

So just to expand on my question a little....

 

Q: Does that mean that there is no real center to a gravity well for a spherical object? it just appears to act that way?

 

 

Q: What would a map of the curve of space due to gravitational forces within a sphere look like? Would the 'deepest' part of the gravity well look similar to smaller hollow sphere within the object?

[mooeypoo]

So just to expand on my question a little....

 

Q: Does that mean that there is no real center to a gravity well for a spherical object? it just appears to act that way?

Center of gravity ? you mean center of mass, I assume? Center of mass does not depend on having actual mass in there, it just defines the point which you would relate to as if all the mass is accumulated there, when you calculate its movement or what and how it affects other objects.

 

For example, if you look at an L shaped object, the center of mass might be at the corner of the L, but towards the 'center' (not 'inside' the material).. that doesn't mean there's MASS there, it just means that when it rotates, or moves, it will go by its 'center' point.

 

Q: What would a map of the curve of space due to gravitational forces within a sphere look like? Would the 'deepest' part of the gravity well look similar to smaller hollow sphere within the object?

I don't understand the question. Curve of space inside the sphere? There's zero net gravity inside the sphere..

[Vortigon]

Center of gravity ? you mean center of mass, I assume? Center of mass does not depend on having actual mass in there, it just defines the point which you would relate to as if all the mass is accumulated there, when you calculate its movement or what and how it affects other objects.

 

For example, if you look at an L shaped object, the center of mass might be at the corner of the L, but towards the 'center' (not 'inside' the material).. that doesn't mean there's MASS there, it just means that when it rotates, or moves, it will go by its 'center' point.

 

 

I don't understand the question. Curve of space inside the sphere? There's zero net gravity inside the sphere..

 

Thanks for your answer I'll try to re-phrase the second question;

 

Q: What I mean is, if we made a 3 dimensional representation of the internal gravitational forces contained within a spherical body in space, such as the Earth, showing the severity of the curvature of space-time due to it's gravity, where and how would the strongest effects be seen? What shape would the strongest areas of effect form in 3 dimensions? Would a hollow sphere within the Earth be representative of the area that has the greatest curvature of space-time?

 

I don't think I explained my question any better actually lol

 

 

I guess I am trying to relate back to the simpler model of gravity that of placing a round object on a blanket which shows how space curves proportional to the mass of the object, and how I could visualise the internal gravitational forces within the earth in a similar type of 3 dimensional way and any shape it may form. Since there is no gravity at the very center etc

[Sisyphus]

The curvature is steepest at the surface. It gets less and less steep the deeper you go, until at the middle it's flat. That's still the deepest part of the gravity well, however. Think of a hill with a rounded top. The ground is horizontal at the top, but it's also the highest point.

 

For a hollow sphere, it's more like a plateau. Like the solid sphere, it's steepest at the outer surface, and gets less steep the deeper you go. Except instead of becoming flat only at the exact center, the entire volume inside the inner surface is flat.

[Vortigon]

The curvature is steepest at the surface. It gets less and less steep the deeper you go, until at the middle it's flat. That's still the deepest part of the gravity well, however. Think of a hill with a rounded top. The ground is horizontal at the top, but it's also the highest point.

 

For a hollow sphere, it's more like a plateau. Like the solid sphere, it's steepest at the outer surface, and gets less steep the deeper you go. Except instead of becoming flat only at the exact center, the entire volume inside the inner surface is flat.

 

Thank you very much!!