What would gravity do at the centre of a hollow Earth?

  • 38 Replies
  • 14355 Views

0 Members and 1 Guest are viewing this topic.

*

Bill Wilker

  • Guest
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?

*

Offline Mr. Scientist

  • Neilep Level Member
  • ******
  • 1451
  • http://www.facebook.com/#/profile.php?ref=profile&
    • View Profile
    • Time Theory
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.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪ē)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

٩๏̯͡๏۶

*

Offline RD

  • Neilep Level Member
  • ******
  • 8185
    • View Profile
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 »

*

Offline Madidus_Scientia

  • Neilep Level Member
  • ******
  • 1451
    • View Profile
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.

*

Offline graham.d

  • Neilep Level Member
  • ******
  • 2208
    • View Profile
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.

*

Offline graham.d

  • Neilep Level Member
  • ******
  • 2208
    • View Profile
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.

*

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
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.
Learn, create, test and tell
evolution rules in all things
God says so!

*

Offline syhprum

  • Neilep Level Member
  • ******
  • 3924
    • View Profile
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
syhprum

*

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
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
Learn, create, test and tell
evolution rules in all things
God says so!

*

Offline LeeE

  • Neilep Level Member
  • ******
  • 3382
    • View Profile
    • Spatial
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/R≤ 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.
...And its claws are as big as cups, and for some reason it's got a tremendous fear of stamps! And Mrs Doyle was telling me it's got magnets on its tail, so if you're made out of metal it can attach itself to you! And instead of a mouth it's got four arses!

*

Offline graham.d

  • Neilep Level Member
  • ******
  • 2208
    • View Profile
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.

*

Offline syhprum

  • Neilep Level Member
  • ******
  • 3924
    • View Profile
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
syhprum

*

Ethos

  • Guest
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 »

*

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
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.
Learn, create, test and tell
evolution rules in all things
God says so!

*

Offline syhprum

  • Neilep Level Member
  • ******
  • 3924
    • View Profile
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 »
syhprum

*

Offline PhysBang

  • Hero Member
  • *****
  • 598
    • View Profile
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.

*

Offline Pmb

  • Neilep Level Member
  • ******
  • 1838
  • Physicist
    • View Profile
    • New England Science Constortium
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

  • Guest
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 ?

*

Offline graham.d

  • Neilep Level Member
  • ******
  • 2208
    • View Profile
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

  • Guest
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 ! 

*

Offline graham.d

  • Neilep Level Member
  • ******
  • 2208
    • View Profile
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

  • Guest
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 ?

*

Offline RAJ1

  • First timers
  • *
  • 5
    • View Profile
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.

*

Offline Phractality

  • Hero Member
  • *****
  • 523
    • View Profile
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 = 2πρr≤δr), use Newton's equation (F = G(m≤/r≤)) 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 »
Imagination is more important than knowledge. Einstein

*

Offline RAJ1

  • First timers
  • *
  • 5
    • View Profile
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. 

newbielink:http://cseligman.com/text/planets/internalpressure.htm [nonactive]

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.

newbielink:http://cseligman.com/text/planets/internalpressure.htm [nonactive]


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 = 2πρr≤δr), use Newton's equation (F = G(m≤/r≤)) 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.

*

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • 12342
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #25 on: 15/04/2011 21:32:37 »
So stay with us and argue Raj, your memory will come back as you find yourself defending your views :) Or you will create new and even more advanced ideas/memories as you find yourself forced to explain your thoughts in detail. It's good for the soul to argue, well, in moderation at least :)
"BOMB DISPOSAL EXPERT. If you see me running, try to keep up."

*

Offline oatman

  • Jr. Member
  • **
  • 16
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #26 on: 16/04/2011 12:21:38 »
I read somewhere this exact scenario was put forward as a means of time travel, hypothetically.

Maybe if you could position yourself right in the centre of some huge object say Jupiter, time would be sufficiently affected by the gravity to make it pass extremely slowly for you.

getting in and out could be a bit tricky though!

*

Offline RAJ1

  • First timers
  • *
  • 5
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #27 on: 19/05/2011 19:22:59 »
Sorry to beat a dead horse here.

But could someone try to explain (simplify) this scenario.

Its hypothetical so for now just ignore what i am about to describe is impossible to do.  Pretend the material is of infinite strength and will not bend or break.

Ok

Lets make a giant ping pong ball with radius of the milkyway.  The thickness will be say 10 feet thick, the center is void of air, just empty space.
The material its made of is the density of a neutron star.

The curvature of the inside wall of the ball would appear flat as a pancake to the observer.   

If you were floating 4 feet from this wall the gravity of the dense material would be very strong.  The gravity of the opposing wall (100,000 light years away) would be very weak in comparison.

I guess i am having a difficult time wrapping my head around the idea that the gravity of the opposing walls (curved) would cancel out the gravity of the wall 4 feet from you.

I know equations will probably say its true.  But could someone explain in simplified terms as to how this would occur.


*

Offline imatfaal

  • Neilep Level Member
  • ******
  • 2787
  • rouge moderator
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #28 on: 19/05/2011 22:31:21 »
Raj - it's non-intuitive but here goes. i don't know where you are - but I live close to St Pauls Cathedral in London - google it and check out the dome (and before anyone says I know it's a fake dome).  Well if you go up to the gallery in the dome you can get a much better impression.  Stand with your back to the centre and you can see 50ish metres squared of wall; but stand with your back to the wall and look across the centre and you can see many thousands of square metres.

Ok now to your sphere. You are floating in your sphere, four feet away is the wall, look up look down look left and right - if you haven't cricked your neck you have looked maybe 45degrees down, up, left and right.  Its quite a small area (relative to the whole sphere) that you have looked at.  If you use your spacesuit jets to spin 180 degrees on your long axis the wall is now 4 feet behind you.  Look up, look down, look left and right.  It's big ain't it. Inside a uniform sphere you can think that the bit of the wall i can see is close but small and pulling me forward; but all the wall I cannot see is faraway but big and pulling me backward.  the two forces balance.

In reality it's not just forward and backwards - but up and down and sideways, but the same thing apples   The amazing thing about Newton's Shell theorem or Gauss's law (same thing different maths) is that small and close balances with massive and far away.


It takes a genius like Newton or Gauss to intuitively understand that this works everywhere in the dome and in 3 dimensions - and then to prove it mathematically.  I hope that has helped - as you move towards the edge the amount of mass pulling you back gets bigger.
Thereís no sense in being precise when you donít even know what youíre talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

*

Offline CZARCAR

  • Hero Member
  • *****
  • 686
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #29 on: 20/05/2011 17:27:02 »
act kinda like the tides of the oceans?

*

Offline RAJ1

  • First timers
  • *
  • 5
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #30 on: 20/05/2011 23:34:54 »
As I move toward the side (4 feet from me) the pull will only become stronger and the pull from the side 100,000 light years away will grow a little weaker.

*

Offline Geezer

  • Neilep Level Member
  • ******
  • 8328
  • "Vive la rťsistance!"
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #31 on: 21/05/2011 03:24:45 »
As I move toward the side (4 feet from me) the pull will only become stronger and the pull from the side 100,000 light years away will grow a little weaker.

If you think of the sphere as being composed of a series of rings, and consider the gravitational force that each ring exerts on you as you approach the smallest ring, you can see that the closer you get to the smallest ring, (which, in the limit would be a point with no mass), there are fewer rings in front of you and more rings behind you. Not only that, but the rings that are behind you have progessively greater masses until they reach the diameter of the sphere. You can imagine that the masses of the rings behind you increase in a very non-linear fashion as you approach the smallest one.

I think that if you sum the forces exerted by all the rings in front of you you will find that it always equals the sum of the forces exerted by all the rings behind you. If you don't know how to do that using calculus, you might try plugging numbers into a fairly crude spreadsheet model (using rather "chunky" rings). In that case the forces won't balance perfectly, but they should be close enough to demonstrate the principle.
There ain'ta no sanity clause, and there ain'ta no centrifugal force śther.

*

Offline imatfaal

  • Neilep Level Member
  • ******
  • 2787
  • rouge moderator
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #32 on: 21/05/2011 15:10:40 »
As I move toward the side (4 feet from me) the pull will only become stronger and the pull from the side 100,000 light years away will grow a little weaker.

nope.  As Gzr said - less of the wall will be pulling you foward and more pulling you back.

1. Restart your thought experiment from the centre.  at the centre you must agree there is no way you can feel a net force - even if this theorem was wrong everything would still balance at the centre.

2. Move a metre in any direction.  You are a metre closer to the wall directly in front - and the force from that will be a little stronger. You are a metre further away from wall directly to the rear - and the force from that will be a little weaker.  BUT - you need to take in the wall above, below, left and right of you.  There is a metre band that was vertically/below/around you - and previously was neither pulling you forward or backwards BUT NOW it is behind you and pulling you back

3. All these little changes balance out.  If you want to prove it to yourself with Gzr's excel model then let us know and I will provide some ideas (you will have to use components of force and trig).  Personally if I was gonna do a little model I would use lots of points rather than rings - but I am a masochist


Thereís no sense in being precise when you donít even know what youíre talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

*

Offline Ken Hughes

  • Full Member
  • ***
  • 56
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #33 on: 21/05/2011 21:04:25 »
Hi Guys,

Interesting discussion. It's forty years since I did my engineering degree so I'm a little rusty on the math. I will have to take your word for the maths predicting neutral gravitation everywhere inside. I can see that within the hollow sphere, if you move slightly from the centre, forward of you there is an increased attraction due to the closer proximity of the shell, but behind you, although the attraction is weaker due to the greater distances, there is nevertheless more mass doing the attracting. I guess what you're saying is the maths proves these effects are equal and opposite and so always provide equilibrium?

I wonder about the pressure effects also. In an actual planet like the Earth, most of it is fluid (apart from the very thin crust), so there will be a pressure build up, even though the gravitation has been reduced to zero at the centre. Also, the gravitational affects will not be zero everywhere, only at the centre, since there is mass all around, not just at the crust, and if you move off centre a little, the large amount of mass behind you and the small mass in front of you, will pull you back to centre. I believe the condition is termed "meta stable". However, you will be crushed to a pulp by the extreme pressure as well as being fried. Personally, I wouldn't try it.

*

Offline Ken Hughes

  • Full Member
  • ***
  • 56
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #34 on: 21/05/2011 22:14:31 »
Hi again,

I see there is a second part to this thread, namely;- which is the best way to keep your domestic water hot;- leaving the heater on all the time or heating it up on a timer to give you the hot water only when you plan to use it.
If I remember correctly, there is a crossover point, depending on the shape and size of the tank, the conductivity of the insulation and the temperatures inside and outside of the tank, where increasing the insulation thickness, simply increases the area of the outside of the insulation which becomes so large that the reduced temperature of the external surface is overpowered by the greater surface area emitting the heat. So, firstly, let's assume the tank and insulation have been designed to avoid this problem, ie we have not wasted money in over insulating the tank and in losing more heat because of this.

In the case where we leave the heater on, we are simply providing energy over time to replace the heat lost through the insulation due to the temperature difference between the insulation surface and the ambient conditions. This is a constant over a given period, ie heat is lost at a constant rate but if the insulation design is good, this will be at a minimum. We also use energy to replace the hot water we use, presumably via a thermostat.

In the other case, where the heater is on a timer, then when the timer switches off, the rate of heat loss starts to reduce proportionate to the cooling of the tank and we save energy since less heat is lost as the tank cools. When the timer cuts in, we heat the tank up again from a lower temperature. This time we replace the reduced heat lost due to radiation, plus the heat in whatever hot water we use.

The answer to the question therefore is;- "IT DEPENDS"    [;D]

It depends on the design of the system and how much and how often you want to use the water. The decision is one of balancing the convenience of having hot water on demand at any time of day or otherwise frequently, against the small savings to be made from the temperature differences between a constantly hot tank and a gradually cooling tank.

Keeping the heater on is very slightly less efficient, but not noticably so. Personally, I always keep the heater on and have never experienced major heating bills compared to people who don't. I always get hot showers, any time I want.

*

Offline imatfaal

  • Neilep Level Member
  • ******
  • 2787
  • rouge moderator
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #35 on: 21/05/2011 23:15:34 »
Hi Ken - Oh Yeah youre right - the hollow earth bit of the thread is a little misleading - the shell has to be uniform and spherically symmetrical too!  Whilst the idea of an enormous spherical sphere is obviously ludicrous - the isotropic and homogeneous layout of space at a large scale means that the Shell Theorem (also called Newton's or Gauss's)  is one of the most basic tools in cosmology - to simplify massively if you are in an enormous cloud of stars and galaxies and it approximates homogeneity (each bit is the same) and isotropy (each direction looks the same) then the shell theorem can apply.
Thereís no sense in being precise when you donít even know what youíre talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

*

Offline Ken Hughes

  • Full Member
  • ***
  • 56
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #36 on: 29/05/2011 14:09:41 »
Hi,

Surely the application of the shell theory to the whole universe has to be an approximation, perhaps practical for very small densities inside the hypothetical sphere?

*

Offline Phractality

  • Hero Member
  • *****
  • 523
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #37 on: 29/05/2011 20:07:24 »
When dealing with the whole universe, you have to make some assumptions, and it is always best to know what your assumptions are and not forget them. A has already been stated, we are assuming the distribution of mass of the universe (at the largest scales) is isotropic and homogeneous. Now, we must decide whether we are looking at a finite quantity of contained within a finite volume of expanding space (which started as a point singularity; i.e. big bang), or whether there is an infinite amount of mass contained in an infinite volume of space (which started at infinite density, but has always been infinitely large), or some other scenario.

In the big bang scenario, the whole space-time continuum is warped by gravity, because there is an outermost hyper-spherical shell, and gravitational potential is a function of 4D distance from the center (i.e. from the big bang). In the second scenario, there is no outermost shell (in any of the four dimensions), gravitational potential is the same everywhere, and so, there is no large-scale warp of the space-time continuum. (It is often said that the calculation of critical density considers only density and not size, but the truth is, the formula is valid only if you assume finite size.)

"Other scenarios" might include: A universe that has always had finite density but infinite size and no beginning or end. A lumpy universe which just happens to be homogeneous and isotropic within our Hubble sphere. Multiverses, God done, it, etc.
Imagination is more important than knowledge. Einstein

*

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • 12342
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
What would gravity do at the centre of a hollow Earth?
« Reply #38 on: 30/05/2011 01:13:01 »
You know Raj, the universe is weird. The idea of 'infinity' applied topologically may just become a dough nut, or a sphere, on where you can walk but never arrive to any endpoint. It's geometries, and as such restricted only by those 'laws' we can think up, allowing topologies to change shape like if twisting/bending them, or turning them inside out, etc.

Newtons shells as I got it.

==


You better read this one too A better explanation :) as mine might seem a little confused. It's not that 'self sufficient'(?) to understand how he thought that masses took themselves out. But he had one direction left in his shell theorem as I understands it? and applied on a universe such a direction must exist too, which it doesn't, as far as I know that is :)
« Last Edit: 30/05/2011 01:29:25 by yor_on »
"BOMB DISPOSAL EXPERT. If you see me running, try to keep up."