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Author Topic: What would gravity do at the centre of a hollow Earth?  (Read 13695 times)

Bill Wilker

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What would gravity do at the centre of a hollow Earth?
« on: 18/10/2009 13:30:04 »
Bill Wilker  asked the Naked Scientists:

Gravity pulls me towards the Earth because it is the closest massive object.  Now, if the very core of the Earth was hollowed out into a sphere 20 feet in diameter and I was placed in the middle, what would the effect of gravity be on me? (We can assume I'm indestructible!)

Would I float in the centre? Gravity should be pulling me nearly equally in each direction, right?

Thanks,

Bill Wilker
Atlanta, Georgia,  US

What do you think?

Mr. Scientist

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What would gravity do at the centre of a hollow Earth?
« Reply #1 on: 18/10/2009 17:00:36 »
Bill Wilker  asked the Naked Scientists:

Gravity pulls me towards the Earth because it is the closest massive object.  Now, if the very core of the Earth was hollowed out into a sphere 20 feet in diameter and I was placed in the middle, what would the effect of gravity be on me? (We can assume I'm indestructible!)

Would I float in the centre? Gravity should be pulling me nearly equally in each direction, right?

Thanks,

Bill Wilker
Atlanta, Georgia,  US

What do you think?

There is a good answer for this. I need to find the physicists paper now... but to give you a general idea, relativity predicts you would be in a perfect state to experience the warping of spacetime around you. You would be enclosed within the potential of the gravitational field.

I'll need to find the paper now... Aharanov i think... hold on.

RD

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What would gravity do at the centre of a hollow Earth?
« Reply #2 on: 18/10/2009 17:27:02 »
Quote from: Bill Wilker  link=topic=26249.msg279892#msg279892 date=1255869004
Would I float in the centre? Gravity should be pulling me nearly equally in each direction, right?

You wouldn't have to be in the centre of the hollow earth for the forces to cancel out ...
http://en.wikipedia.org/wiki/Shell_theorem#Inside_a_shell
« Last Edit: 18/10/2009 17:28:40 by RD »

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What would gravity do at the centre of a hollow Earth?
« Reply #3 on: 18/10/2009 17:29:55 »
Quote
Would I float in the centre? Gravity should be pulling me nearly equally in each direction, right?

Yes, that's correct.

graham.d

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What would gravity do at the centre of a hollow Earth?
« Reply #4 on: 18/10/2009 17:30:25 »
RD is right. Inside a spherical shell the gravitational field is zero everywhere.

graham.d

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What would gravity do at the centre of a hollow Earth?
« Reply #5 on: 18/10/2009 22:43:11 »
Dave, I think you must have made an error. This is a well known fact associated with an inverse square field. It is true of an electric field from a charged sphere too.

Soul Surfer

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What would gravity do at the centre of a hollow Earth?
« Reply #6 on: 18/10/2009 23:23:03 »
The zero gravitiational field inside a uniform spherical shell is one of the important less well understood facts about gravity as is the fact that the gravitiational field inside the earrth or any other reasonably uniformly dense body drops linearly to zero at the centre.  This would also be true of material collapsing inside a black hole at the instant the event horizon first forms.

syhprum

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What would gravity do at the centre of a hollow Earth?
« Reply #7 on: 19/10/2009 06:36:25 »
Yes perhaps counter-intuitively that is the case, at all points inside a uniform hollow sphere gravity is zero

Soul Surfer

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What would gravity do at the centre of a hollow Earth?
« Reply #8 on: 19/10/2009 08:30:52 »
I agree.  It then follows that inside a simple uniform spherical solid body you can ignore the gravitational effect of the spherical shells outside your position it is only the spherical shells between you and the centre of the sphere that give the gravitational field that you would experience.

It also means that in any uniform infinite massive medium the net gravitational field is zero.  It is only irregularities in the density of a large volume of indefinite size (like our universe) that create gravitational forces.

An absolutely uniformly dense massive space will not collapse to form planets stars and galaxies.  This was one of the big problems with the early days of the big bang modelling.  If it was like a normal explosion it would have collapsed into self gravitating lumps very quickly.  It had to be very uniform for very large bodies to form slowly.  The cosmic microwave background then proved that it was incredibly uniform

LeeE

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What would gravity do at the centre of a hollow Earth?
« Reply #9 on: 19/10/2009 12:19:53 »
I can't agree that the gravitational field is zero everywhere in a hollow sphere.  As soon as you move off center, the distance to that side of the sphere will be closer, and the distance to the other side farther.  The 1/Rē effects apply and you get drawn to the closer side.  I confirmed my theory by computing a simple piecewise approximation using Excel.

Yup, as the others have said, gravity is balanced anywhere within a hollow sphere.  When you move off-center, so that you are closer to one side than the other, there is more matter to the distant side than there is to the closer side and this balances out the forces.

graham.d

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What would gravity do at the centre of a hollow Earth?
« Reply #10 on: 19/10/2009 16:17:59 »
We are talking about a gravitational field inside a perfect, non-rotating, spherical shell of any thickness but uniform density. The field due to the shell, within the shell, is everywhere zero. There are no fields, no tidal effects. The size of the body being acted upon is not relevent.

syhprum

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What would gravity do at the centre of a hollow Earth?
« Reply #11 on: 19/10/2009 18:08:21 »
We are assuming there is a vacuum within the sphere presumably if it was filled with fluid or gas objects would gravitate to the centre

Ethos

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What would gravity do at the centre of a hollow Earth?
« Reply #12 on: 19/10/2009 22:32:48 »
This brings to mind another question which has puzzled me over the years. Let's imagine a hole thru the earth, say about 10 feet in dia passing completely thru from one side to the other. Now let's drop a lead ball down the hole. It will accelerate initially and after attaining a substantial velocity ofcourse, it will begin to slow down as it comes closer to the center. My question is this: Will it pass thru the center or will it just slow down and come to a complete stop upon reaching the center.

Ofcourse, if it dosen't stop on the first pass, it will eventually stop as the energy of the system falls to zero. In any case, which of the two processes will happen? Will it stop on the first pass, or will it ociliate back and forth until the kinetic energy is spent?
« Last Edit: 19/10/2009 22:46:29 by Ethos »

Soul Surfer

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What would gravity do at the centre of a hollow Earth?
« Reply #13 on: 19/10/2009 23:07:14 »
If the hole was evacuated it would drop right through from UK to the antipodes going fastest as it passes through the centre and then return precisely to whence it came taking about an hour and a half and gettting up to about 5 miles per second as it passes through the centre of the earth.  if there was air in the hole it would be slowed down very significantly.

syhprum

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What would gravity do at the centre of a hollow Earth?
« Reply #14 on: 20/10/2009 08:54:53 »
The time for a transit to the Antipodes and back is exactly the same as a ground level orbit time i.e approximately 84 minutes.
The path does not have to pass Thru the centre of the Earth the transit time is exactly the same for any tangentle passage on frictionless rails
The transit time Thru any planet or star depends only on its density not its size thru the Sun would take about 55 minutes.

This subject has been extensively discussed before as 'The gravity train'.
« Last Edit: 12/04/2011 22:41:27 by syhprum »

PhysBang

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What would gravity do at the centre of a hollow Earth?
« Reply #15 on: 20/10/2009 13:55:37 »
Then we're talking about a two-body problem involving a perfectly evacuated shell and an object of infintely small mass.  It could not involve the hollowness filled with mass (not even air).  It could not involve an object "floating around inside" whose outer diameter is only, say, 1 micron smaller than the inner diameter of the shell.
Nope. It is a basic theorem, proved by Newton in his Principia, that for a sphere, the outer shell of the sphere, no matter how thick, has no net influence on the contents inside the shell, regardless of their position or composition. If the Earth was perfectly spherical, the net gravitation from its outer shell (defined however you'd like) would have no net gravitational influence on the inner Earth.

The GR equivalent is Birkoff's Theorem.

Pmb

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What would gravity do at the centre of a hollow Earth?
« Reply #16 on: 20/10/2009 14:23:06 »
We are assuming there is a vacuum within the sphere presumably if it was filled with fluid or gas objects would gravitate to the centre
If you're referring to the gravitational force exerted by the gas itself then you're right. If you were to ignore the gravitational forces exerted by the gas then objects wouldn't gravitate to the center. There would be no reason for it to. But if you really are referring to the gravitational pull of the gas then this is no longer a hollow sphere. It's merely a situation where the mass density changes with the radius but with no hollow center. Then its merely a word play on what it means to be "hollow."

Kiran The King Kai

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What would gravity do at the centre of a hollow Earth?
« Reply #17 on: 20/10/2009 15:38:09 »
Guys !

Wait ? Wait ?

Consider this :
By Applying Newton laws of G . forces cancel out !
What about the General relativity ?

graham.d

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What would gravity do at the centre of a hollow Earth?
« Reply #18 on: 20/10/2009 17:20:06 »
Given the assumptions, non-rotating, non-accelerating, perfect spherical (hollow) shell with uniform density and, for the purposes of GR, locally flat space, then it is true in General Relativity too.

Kiran The King Kai

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What would gravity do at the centre of a hollow Earth?
« Reply #19 on: 21/10/2009 09:21:31 »
Given the assumptions, non-rotating, non-accelerating, perfect spherical (hollow) shell with uniform density and, for the purposes of GR, locally flat space, then it is true in General Relativity too.
but it's just a theory !

We always studied external behavior of GR !
we never studied about with happens at its center..

any thing if we are trying to predict in Nature..
might result in fact with our GR or  might fail

Physics is a subject where it always believes in Practical work !
we need to do an experiment on it !
we can't go inside earth but we can try to go at the center of  very big object in space ! like comet !

graham.d

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What would gravity do at the centre of a hollow Earth?
« Reply #20 on: 21/10/2009 13:12:09 »
Kiran, we do know, both from theory and practice, that the field resulting from a spherical shell and inside the shell, for forces obeying the inverse square law, is evrywhere zero. The practical result is obtainable from electrostatics. I doubt there has been any measurement to confirm this with gravity because the apparatus would have to be very large because gravity is such a small force. Nonetheless it has been shown that gravity obeys the inverse square law to high accuracy. It is sufficient to say that it would be very likely to be well behaved and predictable (accurate even with Newtonian mechanics) except in very extreme circumstances. I doubt that even a perfectly hollowed out sphere the size/mass of the earth would show anything significantly different from Newtonian mechanics. Certainly a comet would not and, in any case, where would you get a comet that was perfectly spherical and of perfectly uniform density?

I see no reason to depart from the accepted theories, whether Newtonian or Relativistic, without some reasoned justification for doubting them. I have no doubt that Relativity will get superseded at some point, but I don't think it is likely to be on this basis.

Kiran The King Kai

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What would gravity do at the centre of a hollow Earth?
« Reply #21 on: 23/10/2009 17:35:58 »
Kiran, we do know, both from theory and practice, that the field resulting from a spherical shell and inside the shell, for forces obeying the inverse square law, is evrywhere zero. The practical result is obtainable from electrostatics. I doubt there has been any measurement to confirm this with gravity because the apparatus would have to be very large because gravity is such a small force. Nonetheless it has been shown that gravity obeys the inverse square law to high accuracy. It is sufficient to say that it would be very likely to be well behaved and predictable (accurate even with Newtonian mechanics) except in very extreme circumstances. I doubt that even a perfectly hollowed out sphere the size/mass of the earth would show anything significantly different from Newtonian mechanics. Certainly a comet would not and, in any case, where would you get a comet that was perfectly spherical and of perfectly uniform density?

I see no reason to depart from the accepted theories, whether Newtonian or Relativistic, without some reasoned justification for doubting them. I have no doubt that Relativity will get superseded at some point, but I don't think it is likely to be on this basis.
wow you are cool , are you a Physicist ?

RAJ1

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What would gravity do at the centre of a hollow Earth?
« Reply #22 on: 12/04/2011 22:29:52 »
I do not think this is correct.  Let me illustrate why field is not zero everywhere inside a hollow earth or ball.

Lets take a lead ball the size of the earth

We hollow it out so its thickness is maybe 1 mile thick, so its mostly hollow.  Like a giant tennis ball made of lead.

If you were on the inside 1 foot from the inside wall (many thousands of miles from the center)

Do you think you would be stationary?  Or would you drift to the center or drift towards the inside wall?

Well remember that gravity weakens the further you are away (inverse square)

So the only place where the field cancels is dead center of the hollow sphere.

If you are placed off center by a few feet you will drift towards the outside walls.   The wall you are closest to will have a stronger gravitational field.  Depending on the material the sphere is made of the acceleration would be low and would not be constant.

ie.  If you were in space millions of miles from earth you would not fall at 9.8m/sec2  towards earth (assuming no other planets exist)

For those of you who have played the game Halo.  They used a rotating halo to simulate gravity.  But they also could have made the material (the land) denser so it would have enough gravity to hold you to it.   It if were neutron star material it might be a bit too much.  But you get the idea.

=================================================================================================================================================
We are talking about a gravitational field inside a perfect, non-rotating, spherical shell of any thickness but uniform density. The field due to the shell, within the shell, is everywhere zero. There are no fields, no tidal effects. The size of the body being acted upon is not relevent.

Phractality

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What would gravity do at the centre of a hollow Earth?
« Reply #23 on: 12/04/2011 23:29:53 »
RAJ1, when you study tripple integrals in college, one of your homework assignments will be to integrate Newton's law of gravity for a uniform hollow sphere. When you do so, you will discover for yourself that the field inside the sphere is zero, and outside it is the same as if all the mass were concentrated at the center. Until you discover it for yourself, you'll just have to take the word of your seniors.

As for general relativity, it yields exactly the same results as Newtonian physics except in extreme cases, like black holes and the whole universe. A hollow Earth is not such an extreme case.

The reason the Earth can't be hollow is because two halves of the hollow sphere would be attracted to one another. The pressure where two halves meet would be greater than the strength of the material. So pieces would break off and float inside, where they would be attracted to each other's gravity and form a solid ball. That ball would attract other chuncks from the near side of the hollow sphere, and very quickly the whole thing would collapse into one solid ball.

A small sphere can be made of just about any solid, but when you get to the radius of Earth, it would need to be quite strong. You can do the math yourself; it's pretty simple. Consider two hemispherical shells of a given thickness and radius. The center of mass of a thin hemisphere is located midway between the center and the surface. Calculate the mass of each hemisphere (m = 2πρrēδr), use Newton's equation (F = G(mē/rē)) to get the force of gravity and divide by the area (a = 2πrδr) where the two hemispheres meet. That will give you the compressive pressure. Compare that to a table of the compressive strenghts of various materials.
« Last Edit: 12/04/2011 23:32:32 by Phractality »

RAJ1

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What would gravity do at the centre of a hollow Earth?
« Reply #24 on: 13/04/2011 00:34:21 »
Phractality,  thanks for the response.

I see the error in the logic and looked at some equations.   I'd seen this  question posted a few places and never saw anyone give a detailed explanation.  I would like you to take a look at this site and see what ya think.

My error was not factoring in that while you could be closer to the inside wall of the sphere the area or mass to the side furthest from you would be weaker but the amount of mass is larger. (ie. weaker but more numerous gravity vectors which as a whole will cancel out the force to your right.  I'm not sure that made sense but there is a good diagram and explanation as to why.  And of course newtons equations also fit in with that.

Yes I know there would be a maximum size before the planet or object would break apart.  Wonder how big it would be for say a iron ball.

I was a physics major in undergrad, had a bout of encephalitis recently and lost memory, its still coming back so I have to relearn many things.  I still like it but obviously my logic is not what it use to be.

Thanks for the help.

Let me know if that is a good page in your opinion.

RAJ1, when you study tripple integrals in college, one of your homework assignments will be to integrate Newton's law of gravity for a uniform hollow sphere. When you do so, you will discover for yourself that the field inside the sphere is zero, and outside it is the same as if all the mass were concentrated at the center. Until you discover it for yourself, you'll just have to take the word of your seniors.

As for general relativity, it yields exactly the same results as Newtonian physics except in extreme cases, like black holes and the whole universe. A hollow Earth is not such an extreme case.

The reason the Earth can't be hollow is because two halves of the hollow sphere would be attracted to one another. The pressure where two halves meet would be greater than the strength of the material. So pieces would break off and float inside, where they would be attracted to each other's gravity and form a solid ball. That ball would attract other chuncks from the near side of the hollow sphere, and very quickly the whole thing would collapse into one solid ball.

A small sphere can be made of just about any solid, but when you get to the radius of Earth, it would need to be quite strong. You can do the math yourself; it's pretty simple. Consider two hemispherical shells of a given thickness and radius. The newbielink:http://thesaurus.maths.org/mmkb/entry.html;jsessionid=D9BBC8A1DCD98DE74989381B0B0A23AC?action=entryByConcept&id=3610&langcode=en [nonactive] is located midway between the center and the surface. Calculate the mass of each hemisphere (m = 2πρrēδr), use Newton's equation (F = G(mē/rē)) to get the force of gravity and divide by the area (a = 2πrδr) where the two hemispheres meet. That will give you the compressive pressure. Compare that to a table of the compressive strenghts of various materials.

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What would gravity do at the centre of a hollow Earth?
« Reply #24 on: 13/04/2011 00:34:21 »