[Bill Wilker]

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]

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]

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

[Madidus_Scientia]

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

Yes, that's correct.

[graham.d]

RD is right. Inside a spherical shell the gravitational field is zero everywhere.

[graham.d]

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]

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]

Yes perhaps counter-intuitively that is the case, at all points inside a uniform hollow sphere gravity is zero

[Soul Surfer]

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]

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/R² 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]

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]

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]

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?

[Soul Surfer]

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]

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'.

[PhysBang]

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]

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]

Guys !

Wait ? Wait ?

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

[graham.d]

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]

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 !