How would gravity behave inside a hollow planet?

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Offline Spacetectonics

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How would gravity behave inside a hollow planet?
« on: 30/12/2012 13:31:16 »
Suppose one day human technology advance to the stage of make him able removing the inner core of the earth(Just imagine) .
Radius of earth is almost 6378 KM suppose we take The inner core out and create an empty space 6378-1300(inner core) = 5078 KM,all (i.e.) from the surface to the bottom of the outer core.

Imagine a man at the center of the earth standing on a artificial platform releasing a ball ( empty space each side), what would happen to the ball?!

The point I wish to confirm here is "what is the gravity inside the earth " is it zero? what about the sun effective gravity? shouldn't the ball follows the space time curvature of the sun if G at the center is zero?!

Cheers,
No conspiracy comments please!!
« Last Edit: 01/01/2013 22:23:54 by chris »

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Offline syhprum

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Re: Gravity inside an empty Planet!
« Reply #1 on: 30/12/2012 14:43:08 »
A vital part of the problem has been left out what has become of the removed materiel has it been ejected to outer space hence reducing the mass of the Earth or has it been spread evenly on top.
The man at the centre would be in a zero gravity situation and would need magnetic boots to stay in contact with his platform and if he merely released his ball it would just float with him.
If he threw it we might be able to do some calculations if we knew what effect the evacuation had had on the mass of the Earth and its initial velocity and its mass relative to the man plus platform. 
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Offline Phractality

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Re: Gravity inside an empty Planet!
« Reply #2 on: 31/12/2012 19:38:47 »
The Earth's crust is thin like the peel of an apple. It is only about .003 of Earth's mass. If you had that amount of mass in a perfectly spherical hollow ball, floating in interstellar space away from any stars or planets, the gravity at the surface would be about .0015 g (because the crust is about half as dense as the rest of the planet). Anywhere inside the ball, the gravity would be precisely zero. That includes anywhere on the inside surface of the ball; so an object floating inside would simply bounce off the inside wall and keep floating.

Multiple objects inside the ball would feel each others gravity and orbit one another. Collisions would cause them to eventually collapse into a single ball, still floating weightlessly inside the Earth-size ball.

The average thickness of Earth's crust, is about 20 km; the circumference is 40,000 km. A bisecting cross section of the crust has an area of about 20 km * 40,000 km = 800,000,000 km2 = 8 x 1014 m2. The force holding the two halves apart against each others gravity is about

1022 kg x .015 n/kg = 1.5 x 1021 n.

So the pressure between the two halves is 1.5 x 1021/ 8 x 1014 ≈  2 x 106 n/m2. = 2 MPa = 200 tonne/m2 ≈  300 psi. The compressive strength of granite is about 100 times greater than that. Therefore, it is conceivable that such a structure made of homogeneous rock could support its own weight, provided that it is perfectly spherical.

If you increase the size and/or mass until you get 1 g (9.8 n/kg) of gravity at the surface, your hollow shell would need to be made of a strong substance to support its own weight. If the density is the same as that of Earth's crust, the pressure would be about 200,000 psi. If my calculations are correct (big IF) such a shell made of aluminum alloy would have plenty of strength to spare, perhaps 100 times more strength than required. The down side of that is that it would need to be at least four times the mass of Earth. Where you gonna find that much aluminum? 

Placing the hollow ball near a star, yes; gravity inside the ball would follow the space-time curvature of the star's gravity. A mass inside the hollow sphere would orbit the star, just as the hollow sphere orbits the star. Zero gravity inside a hollow sphere refers only to gravity resulting from the presence of the hollow sphere, not to gravity resulting from anything outside the sphere. Because of the sun's gravity, such a sphere orbiting the sun would be distorted by the sun's gravity. If it had a daily rotation, tidal forces would bend the spherical shell. If it is made of rock, it will crack, and pieces will break off on the inside.

Those pieces will gravitate toward one another, eventually forming one large ball inside the hollow sphere. As that ball nears the inner surface of the hollow sphere, the gravity of the inside ball will break off more pieces of the outer ball, and eventually, the outer ball will collapse catastrophically. This is one good reason that there are no hollow planets. An even better reason is the difficulty of constructing a hollow planet, in the first place. Even in inner stellar space, there are insurmountable difficulties in creating a large hollow sphere. Near a star or another planet, even a perfectly spherical hollow planet would soon collapse.
« Last Edit: 31/12/2012 19:44:02 by Phractality »
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Offline evan_au

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Re: Gravity inside an empty Planet!
« Reply #3 on: 01/01/2013 00:37:18 »
Quote
Re: shouldn't the ball follow the space time curvature of the sun if G at the center is zero?!

Yes, the hollow Earth would follow the space time curvature of the sun, and will orbit the Sun in a circular 1-year orbit, as if all its (remaining) mass were concentrated at the center.

The weightless man in the center of the hollow Earth, floating near his weightless platform and weightless ball would all also follow the same space time curvature of the sun, and will also orbit the Sun in a 1-year circular orbit.

If the man could hold his breath for a whole year, he may be able to see the effects of the initial separation of man, platform and ball; since they all start off with slightly different distances from the Sun and slightly different velocities, some of the orbits around the Sun will be slightly more elliptical than others, so they will orbit around each other with a roughly 1-year period (in addition to orbiting around each other due to their very small gravitational attraction to each other).

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Offline syhprum

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Re: Gravity inside an empty Planet!
« Reply #4 on: 01/01/2013 11:04:11 »
Would not the Moon orbiting the Earth produce a large amount of movement of the man/ball/platform combination especially if the mass of the Earth has been much reduced by de-gutting it.   
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Offline Pmb

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Re: Gravity inside an empty Planet!
« Reply #5 on: 01/01/2013 13:04:04 »
If the shell that was left didn't collapse then the gravitational field inside the hollow shell is zero, so long as this inner shell's center has the same center as the earth. If a hollow shell is dug out of the Earthy but its center is not at the center of the Earth then there'd be a gravitational field inside.

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Offline Spacetectonics

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Re: Gravity inside an empty Planet!
« Reply #6 on: 01/01/2013 14:02:02 »
Thanks, there are some points behind this question which I am interested and I will go through them gently! (Please consider everything solid and environment (idealized) perfect!),
ok in this case the inner core is almost 1/6 of the thickness of the planet earth, and the hollow area has 1220 KM http://en.wikipedia.org/wiki/Inner_core [nofollow]

radius (compare to 6378 KM earth radius)so there is huge amount of mass all around that ball.
What I understood is floating of that ball in zero G hollow (at the center), now Imagine That ball sits at one side (bottom of) outer core, if we look at the symmetry of the earth in that case, distance between ball and landing site is zero, based on the arguments so far that ball could not walk at the surface of the hollow if she had two foot (under gravity regime)?

 Imagine the earth ďas a centrifuges machine ďthen what will happen for that force? (Spinning around sun @ 30km/s; beside the rotation on 30 degree axis)

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970401c.html [nofollow]

http://ask.yahoo.com/20020411.html [nofollow]

http://www.esri.com/news/arcuser/0610/nospin.html [nofollow]

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Offline syhprum

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Re: Gravity inside an empty Planet!
« Reply #7 on: 01/01/2013 16:06:43 »
If the mass of the Earth has been much reduced by de-gutting the centre of gravity of the Earth Moon system will now be moved much nearer the  moon and the Earth can be considered as a satellite of the Moon.
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Offline Atomic-S

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Re: How would gravity behave inside a hollow planet?
« Reply #8 on: 02/01/2013 05:07:07 »
Spacetectonics:
I don't know if I quite understand you, but if you are speaking of removing the Earth's mantle, leaving only the inner core and the crust, so that the inner core is able to move around in the much larger hollow crust, the first principle that applies is that the crust exerts zero gravitational force on the core, no matter where the core happens to be located inside. By Newton's first law, the core likewise exerts zero net force on the crust. Therefore, the motion of the one has no effect on the motion of the other, so long as they do not touch. (It is here assumed that the effects of Einsteinian general relativity can be ignored.) Likewise, the crust and core may spin in any direction they want, and there is no interaction. If this system is now set in orbit around the sun, each of these objects will orbit as if the other did not exist, the only requirement being that the orbits must match closely enough that the inner core does not slam into the crust. If the system moves in a complex path involving both the sun and moon, again, the core and crust will each travel independently, ignoring the other. They really don't see each other at all.
 

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Offline Spacetectonics

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Re: How would gravity behave inside a hollow planet?
« Reply #9 on: 02/01/2013 07:16:27 »
Thanks,

I reckon it is a good idea to go through the subject you have brought up(at the moment we have only removed the Inner core;1220KM; and the rest including Outer core ,mantle and crust are untouched .so we still have lots of mass around) ,although at this stage what I wish to understand is the consequences of "Centripetal force and Centrifugal force" and what we expect to see from these two at the above case ?(whether they are active in no G? )

I sort of understand comparing the above case to the astronauts in ISS, but just wondering how we deal with the earth rotation speed around the sun and almost 5000Km of mass around that ball.if you know what I am mean?!

Cheers
« Last Edit: 02/01/2013 07:18:40 by Spacetectonics »

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Offline Soul Surfer

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Re: How would gravity behave inside a hollow planet?
« Reply #10 on: 03/01/2013 10:30:21 »
The gravitational attraction inside a massive thick hollow spherical shell is zero everywhere inside the shell. outside of the shell it is as if all the mass of the shell was concentrated at the centre of the shell.  This is one of the more counterintuitive aspects of an inverse square force.  There are lots more that people tend not to realise.
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Offline Spacetectonics

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Re: How would gravity behave inside a hollow planet?
« Reply #11 on: 03/01/2013 18:42:37 »
The gravitational attraction inside a massive thick hollow spherical shell is zero everywhere inside the shell. outside of the shell it is as if all the mass of the shell was concentrated at the centre of the shell.  This is one of the more counterintuitive aspects of an inverse square force.  There are lots more that people tend not to realise.

Thank you Soul Sufer,

Base on the above ,we should not expect to see "Centripetal force and Centrifugal force" either?

Cheers


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Offline Spacetectonics

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Re: How would gravity behave inside a hollow planet?
« Reply #12 on: 04/01/2013 08:48:54 »
The gravitational attraction inside a massive thick hollow spherical shell is zero everywhere inside the shell. outside of the shell it is as if all the mass of the shell was concentrated at the centre of the shell.  This is one of the more counterintuitive aspects of an inverse square force.  There are lots more that people tend not to realise.

Thank you Soul Sufer,

Base on the above ,we should not expect to see "Centripetal force and Centrifugal force" either?

Cheers


Gravity at center of the earth is zero, inside the hollow sphere.

Inner core meant to be solid and outer core liquid.(The low viscosity of the outer core is important in seismology because low-viscosity fluids can not sustain shear stresses)

(The last layer is the core, which is separated into the liquid outer core and the solid inner core)

Source:  http://scign.jpl.nasa.gov/learn/plate1.htm [nofollow]



Consequently if all above are correct, then inner core should free to bounce at the bottom of the mantle (within the outer core) when outer core is liquid?!!
In the other word "inner core" must be free to bounce if "needed"

Or I underestimated the "Internal Perussure"?!

(The Earth's fluid outer core is in vigorous convection through much of the Earth's history. In addition to generating and maintaining Earth s time-varying magnetic field (geodynamo), the core convection also generates mass redistribution in the core and a dynamical pressure field on the core-mantle boundary (CMB))

http://ntrs.nasa.gov/search.jsp?R=20040171502 [nofollow]

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Offline Phractality

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Re: How would gravity behave inside a hollow planet?
« Reply #13 on: 07/01/2013 22:35:36 »
If you removed the outer core, you would relieve the pressure which makes the inner core a pressure solid. The inner core would become liquid until it cools enough to become a regular solid, as opposed to a pressure solid.

When a solid ball is outside a hollow ball, each will orbit the barycenter of the pair. When the solid ball is inside the hollow ball, each member of the pair will orbit whatever third body is nearby, as if the other member of the pair was not there. If the orbits are not perfectly circular and concentric, there will be collisions between the inner and outer balls.

The solid ball floating inside the hollow ball will have no net effect, but when not centered, it will have tidal effects  on the hollow ball.
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Offline Thibeinn

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Re: How would gravity behave inside a hollow planet?
« Reply #14 on: 24/07/2013 16:55:36 »
Spacetectonics,
 
Such a statement as, "gravity inside a hollowed out planet is zero", is scientifically unsound.
 
The truth is that gravity "pulls" toward mass regardless of the mass' orientation or configuration.  Thus, there would also be gravity inside the hollow "pulling" toward the inner surface.  At the exact center point, the gravity would be "pulling" in every direction equally.
 
Assume, for example, the earth was a perfect hollow sphere and the ball perfectly spherical.  If you placed the ball perfectly at the center point (with the ball's center point colocated with the hollow sphere's), the ball would "feel" equal gravitational pull in all directions and would not move (tho if weakly enough constructed it would be pulled apart with the result that the pieces would then be "pulled" to the inner surface in various directions).
 
If however, the ball was placed just slightly off center (or completely off center), it would be "pulled" (in the direction it is off) and toward a specific point on the inner surface.
 
So for future reference, gravity does not only "pull" in an inward direction toward a center point, it "pulls" toward mass regardless of the mass' orientation or configuration.  This is scientific fact.

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #15 on: 24/07/2013 17:38:07 »
Quote from: Spacetectonics
Radius of earth is almost 6378 KM suppose we take The inner core out and create an empty space 6378-1300(inner core) = 5078 KM,all (i.e.) from the surface to the bottom of the outer core.
I find that description to be very confusing. Please rephrase it more clearly.

Quote from: Spacetectonics
Imagine a man at the center of the earth standing on a artificial platform releasing a ball ( empty space each side), what would happen to the ball?!
Nothing. It would float there.

Quote from: Spacetectonics
The point I wish to confirm here is "what is the gravity inside the earth " is it zero? what about the sun effective gravity? shouldn't the ball follows the space time curvature of the sun if G at the center is zero?!
That depends. Suppose you were to hollow out a spherical cavity which is completely contained within the original sphere. If the center of the sphere is the same as the center of the cavity then thereíd be no gravitational field anywhere inside the cavity. If the center of the cavity is offset from the center of the sphere the thereíd be a uniform gravitational field inside the cavity. The strength of the field is proportional to the distance of the center of the cavity to the center of the sphere. For proof please see
http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm

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Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #16 on: 24/07/2013 20:27:15 »
Spacetectonics,
 
Such a statement as, "gravity inside a hollowed out planet is zero", is scientifically unsound.
 
The truth is that gravity "pulls" toward mass regardless of the mass' orientation or configuration.  Thus, there would also be gravity inside the hollow "pulling" toward the inner surface.  At the exact center point, the gravity would be "pulling" in every direction equally.
 
Assume, for example, the earth was a perfect hollow sphere and the ball perfectly spherical.  If you placed the ball perfectly at the center point (with the ball's center point colocated with the hollow sphere's), the ball would "feel" equal gravitational pull in all directions and would not move (tho if weakly enough constructed it would be pulled apart with the result that the pieces would then be "pulled" to the inner surface in various directions).
 
If however, the ball was placed just slightly off center (or completely off center), it would be "pulled" (in the direction it is off) and toward a specific point on the inner surface.
 
So for future reference, gravity does not only "pull" in an inward direction toward a center point, it "pulls" toward mass regardless of the mass' orientation or configuration.  This is scientific fact.

Wrong.
As soul surfer pointed out
"The gravitational attraction inside a massive thick hollow spherical shell is zero everywhere inside the shell. outside of the shell it is as if all the mass of the shell was concentrated at the centre of the shell.  This is one of the more counter-intuitive aspects of an inverse square force.  There are lots more that people tend not to realise."
It seems that, while Newton proved this centuries ago, people refuse to believe it.
http://en.wikipedia.org/wiki/Shell_theorem

« Last Edit: 24/07/2013 20:29:43 by Bored chemist »
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Offline Thibeinn

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Re: How would gravity behave inside a hollow planet?
« Reply #17 on: 24/07/2013 20:56:07 »
The gravity outside the hollow planet "pulls" toward the center.

And, given the fact that gravity always "pulls" toward mass regardless of the orientation or configuration of the mass, inside a hollow planet gravity also "pulls" toward the inner surface.

Gravity is not dependent upon a center point to "pull" towards as a requirement for it's manifestation nor its continuance.

If there is no mass floating at the center point within a hollow planet then there is no mass for gravity to "pull" toward that center point.

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #18 on: 24/07/2013 21:30:02 »
Quote from: Thibeinn
The gravity outside the hollow planet "pulls" toward the center.
So long as you keep in mind that this only holds outside of the shell. It does not hold inside the shell.

Quote from: Thibeinn
And, given the fact that gravity always "pulls" toward mass regardless of the orientation or configuration of the mass, inside a hollow planet gravity also "pulls" toward the inner surface.
Thatís wrong. Each particle is attracted by every other particle by Newtonís law of gravity between two point particles. When the particle is inside the shell all the forces due to the particles which make up the shell cancel out resulting in a gravitational field of zero everywhere inside the shell. If you had or have another way of thinking of how it may work then youíre quite wrong. This fact is demonstrated by every single physics student at least once before he gets his Bachelorís degree. I promise you that.

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Offline Thibeinn

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Re: How would gravity behave inside a hollow planet?
« Reply #19 on: 24/07/2013 22:38:38 »
Thatís wrong. Each particle is attracted by every other particle by Newtonís law of gravity between two point particles. When the particle is inside the shell all the forces due to the particles which make up the shell cancel out resulting in a gravitational field of zero everywhere inside the shell. If you had or have another way of thinking of how it may work then youíre quite wrong. This fact is demonstrated by every single physics student at least once before he gets his Bachelorís degree. I promise you that.

You are mistaken.

Also, just exactly how does a physics student produce a gravitational field in order to demonstrate that?  You mean they solve one or more equations concerning a gravitational field.  Solving an equation does not demonstrate a thing.  It only shows the solving of an equation thought to express/explain a thing in mathematical form.


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Offline JP

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Re: How would gravity behave inside a hollow planet?
« Reply #20 on: 24/07/2013 22:55:41 »
Thibeinn-- Soul Surver, Bored Chemist and Pmb all have enough scientific training to know what they're talking about.  I do as well, and they are absolutely correct.  If you don't believe this, then I'm sure one or more of us would be happy to go through it in more detail, but if you tell us we're wrong, you either: (a) don't understand gravity or (b) don't believe the accepted science of gravity.  If (a), then please take time to enter a discussion about what you don't understand.  If (b), then there is a New Theories section to discuss what you don't believe about the accepted theories. 
« Last Edit: 25/07/2013 15:10:23 by JP »

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #21 on: 24/07/2013 23:31:37 »
Quote from: Thibeinn
You are mistaken.
Itís inappropriate to merely make a claim that others are wrong unless you are prepared to prove your claim. Are you prepared to do that?

And it is you, sir, who are mistaken. What leads you to believe that it is you who is right rather than the rest of the physics community that is wrong? What training in physics do you have?

Quote from: Thibeinn
Also, just exactly how does a physics student produce a gravitational field in order to demonstrate that?  You mean they solve one or more equations concerning a gravitational field.  Solving an equation does not demonstrate a thing.  It only shows the solving of an equation thought to express/explain a thing in mathematical form.
Itís demonstrated from the fact that Newtonís law of gravitation has been verified to very high accuracy. The precise prediction of planetary orbits proves that. There have also been laboratory experiments done which confirm the inverse square law of gravitation and the law of superposition. These facts are used by undergraduate physics students to demonstrate that the gravitational field inside a hollow sphere is zero.

As I said, every undergraduate physics student has demonstrated this at least once as an undergrad. Why you thought that meant a laboratory experiment is beyond me. Iím talking about proof by starting with the well tested theory and doing the actual calculation. If you think thereís no reason to assume that the theory is right then I suggest that you post that in the new theory section like JP suggested. This forum is for well accepted, i.e. orthodox, theories of physics. Not your own pet theory or your disbelief that current theory is wrong.

In any case the proof has been given to you in a previous post. It proves what we said is true given that Newton's law between two point particles is true. That's been verified in the lab too. An outline of experimental resus to date is given in Gravitation and Spacetime - 3rd Ed. by Hans C. Ohanian and Remo Ruffini (2013) in section 1.2.

What are your objections based on rather than merely disagreeing with us?
« Last Edit: 25/07/2013 00:21:11 by Pmb »

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Offline Thibeinn

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Re: How would gravity behave inside a hollow planet?
« Reply #22 on: 25/07/2013 00:09:26 »
As I am new here, I was unaware of a "New Theories" section.  I happened upon this forum by way of a search on the topic of "hollow planet" and got involved in the discussion.  So sue me for presenting my opinion and my argument in defense of it when it was challenged.

I will move on to the "New Theories" section.

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #23 on: 25/07/2013 00:26:52 »
As I am new here, I was unaware of a "New Theories" section.  I happened upon this forum by way of a search on the topic of "hollow planet" and got involved in the discussion.  So sue me for presenting my opinion and my argument in defense of it when it was challenged.

I will move on to the "New Theories" section.

Nobody has ever gotten blamed for arguing their point if it was a valid argument. But nobody accepts arguments of the form "I'm right and you're wrong" and them makes no valid attempt to demonstrate what they claim.

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Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #24 on: 27/07/2013 14:27:01 »
It is manifestly absurd to say "in my opinion, 1+1 =3": you can't have an opinion about matters of fact.
And it is equally absurd to say what Thibeninn said about gravity because that assertion was proven false centuries ago.
And to continue to say it, after that proof has been pointed out is just silly.
« Last Edit: 27/07/2013 14:30:07 by Bored chemist »
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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #25 on: 27/07/2013 15:57:28 »
It is manifestly absurd to say "in my opinion, 1+1 =3": you can't have an opinion about matters of fact.
And it is equally absurd to say what Thibeninn said about gravity because that assertion was proven false centuries ago.
And to continue to say it, after that proof has been pointed out is just silly.
People who don't know calculus can't follow the derivation. But to think that everyone of us who can have all made the exact mistake is hillareously silly.

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lean bean

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Re: How would gravity behave inside a hollow planet?
« Reply #26 on: 27/07/2013 17:16:34 »
Thibeinn, you may find these links interesting
Quote
In the same way, one can show that inside the hollow interior of a spherical shell (or any other spherically symmetric hollow mass configuration), there are no gravitational forces at all.
From  http://www.einstein-online.info/spotlights/gravity_of_gravity

Quote
Gravitation Inside A Uniform Hollow Sphere
The gravitational force inside a hollow sphere shell of uniform areal mass density is everywhere equal to zero, and may be proved by the following argument:
from http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/grvtysp.htm

Quote
The net gravitational force on a point mass inside a spherical shell of mass is identically zero!
From http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.html

Quote
Field Inside a Spherical Shell
This turns out to be surprisingly simple!  We imagine the shell to be very thin, with a mass density  kg per square meter of surface. Begin by drawing a two-way cone radiating out from the point P, so that it includes two small areas of the shell on opposite sides: these two areas will exert gravitational attraction on a mass at P in opposite directions.  It turns out that they exactly cancel.
From http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm


« Last Edit: 27/07/2013 17:20:12 by lean bean »

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Offline evan_au

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Re: How would gravity behave inside a hollow planet?
« Reply #27 on: 28/07/2013 01:18:23 »
Most of the demonstrations of Newton's laws (and Einsteins) have been done from outside a massive object, due to experimental simplicity.

BC's Shell Theorem Link had an interesting note at the bottom, which says that if you could perform the test inside a hollow ball, you may be able to measure something that looks like Einsteins cosmological constant. But the logistics of creating a massive hollow ball far exceeds today's Engineering capabilities!

See: http://en.wikipedia.org/wiki/Shell_theorem#Converses_and_generalisations

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #28 on: 28/07/2013 02:40:57 »
Most of the demonstrations of Newton's laws (and Einsteins) have been done from outside a massive object, due to experimental simplicity.

BC's Shell Theorem Link had an interesting note at the bottom, which says that if you could perform the test inside a hollow ball, you may be able to measure something that looks like Einsteins cosmological constant. But the logistics of creating a massive hollow ball far exceeds today's Engineering capabilities!
I disagree. It's easy to create a hollow shell. Just get a small asterod and make it spherical and then hollow it out. It can be done. It's just not something anybody would want to do because nobody who knows anything about gravity doubts it. One could make a sphere on earth and then measure the field inside and compare it to what the field is like when the shell isn't there. It should be the same. I believe we can make measurements of the gravitational field that accurately

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #29 on: 28/07/2013 05:59:45 »
Iím going to take another shot at this in hopes Thibeinn just isnít seeing what we all know intuitively and from knowing how these things work out in calculations.

Quote from: Thibeinn
Such a statement as, "gravity inside a hollowed out planet is zero", is scientifically unsound.
Do you know what the term ďunsoundĒ means? It means ďnot true.Ē This means that you know of a hollow shell in which the gravitational field was not zero. Otherwise itís theoretical and thereís no reasoning that can lead to such a theoretical prediction.

Newtonís law states that if you have two objects which are small enough to be approximated as point objects and if one of mass m1 and the other has mass m2 then the force on object 1 due to object 2 has the magnitude

F = G m1 m2/r[sup2[/sup]

Where r is the distance between the centers of the objects. This is true regardless of what lies in-between the two objects so long as the gravitational force of what lies in between is taken into account. The direction of the force directed from object 2 to object 1. If there are other bodies whose sizes can be neglected them the principle of superposition applies.

In order to determine the gravitational field inside a hollow shell of mass one calculates the force by considering a large number of small pieces of the shell and let the size of the shell go to zero as the number of pieces goes to infinity and you add up all the contributions. This process is called ďintegrationĒ and is a process invented by Newton for these very kinds of purposes.

Quote from: Thibeinn
The truth is that gravity "pulls" toward mass regardless of the mass' orientation or configuration.
Thatís incorrect. Gravity pulls in the direction that is determined by the gravitational pull of all the objects around it, the forces adding vectorally. If the particle is in the center of a hollow shell its easy to show that all the masses which make up the shell pull on the particle inside the shell in a way that all the forces acting on it cancel out.

If you donít believe this then right a computer program and have it calculate if for you by arranging a shell of a large number of point particles at equal distance from the origin of the coordinate system. Do you know how to write a computer program. If you donít then do you know someone who does? If so then write the program or have someone write it for you. The math necessary to do this is very simple and requires simple algebra and trigonometry. So little is required that it would only take a few weeks to learn it.

So do it and prove the entire physics community wrong! Youíll win a Nobel Prize in physics. Unless you donít think its worth the effort to actually determine the quantity for yourself?

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Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #30 on: 28/07/2013 13:56:48 »
Most of the demonstrations of Newton's laws (and Einsteins) have been done from outside a massive object, due to experimental simplicity.

BC's Shell Theorem Link had an interesting note at the bottom, which says that if you could perform the test inside a hollow ball, you may be able to measure something that looks like Einsteins cosmological constant. But the logistics of creating a massive hollow ball far exceeds today's Engineering capabilities!
I disagree. It's easy to create a hollow shell.
For a certain definition of "easy".
Please disregard all previous signatures.

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Re: How would gravity behave inside a hollow planet?
« Reply #31 on: 28/07/2013 15:59:14 »
Quote from: Bored chemist
For a certain definition of "easy".
Why is it beyond our engineering capabilities to fabricate a hollow shell of steel one meter thick with a radius of 20 meters? A an engineering feat that's easy by any definition in my humble opinion. It's measuring the gravitational field to high precision that's hard.

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Re: How would gravity behave inside a hollow planet?
« Reply #32 on: 28/07/2013 16:22:28 »
Thibeinn Ė If we seem to come off in a bad way then know that we donít intend to be mean in any way. From what you told us you came here to discuss the gravitational field inside a hollow sphere. We said what we did because we know that there is so much scientific evidenced based on observation that to say that the gravitational field inside a spherical shell of uniform mass density is zero that itís taken as a fact. Itís as much of a fact as the fact that Newtonís Laws and Keplerís laws are accurate to a very high degree of accuracy. Those too are based on observation of the solar system.

When you go some place to argue a point then if there is overwhelming evidence against your belief you can expect an argument against it from those of us who chose to do this as a living. That means we spent many years studying the physics and math and spent many grueling hours working out exercise problems and following well-known proofs of these kinds of things. Weíre not new to this picnic. We are all very skilled as to what can be considered a difference of opinion to a difference in a belief. And this is not something that is subject to opinion. Itís something subject to belief. And we have overwhelming reasons to believe what we do and to recognize the errors in your argument. So this is not a personal thing. Weíre not here to be jerks. Some of us, such as myself, are here to help others understand physics and the math that it requires to understand it fully. To say that thereís a gravitational field inside the sphere is like someone telling a seasoned mechanic that a radiator belt is made of leather and has a buckle. Now thatís not a matter of opinion is it? Have you ever looked under the hood of all cars ever built to make sure the mechanic is right when he tells that person heís wrong? :)

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Offline Soul Surfer

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Re: How would gravity behave inside a hollow planet?
« Reply #33 on: 28/07/2013 18:43:20 »
Have just caught up with this the fact that the gravitational field inside a uniform hollow shall is zero everywhere is as I said at first very counterintuitive.  Let me try to explain in non mathematical terms

It is easy to see that the force in the centre is zero because in each small solid angle there is exactly the same amount of material at the same distance. 

It is also easy to see that for any point along a radius from the centre, (this is the only possible position any particle can have inside a spherical cavity) because of the symmetry that the forces perpendicular to the radius line are zero because of the symmetry with equal masses at equal distances in all directions.

All that now remains are the forces along the line from the radius from the centre to the edge. Consider now the gravitational forces generated in a point just inside the surface of the hollow sphere. Let us say the shell is "thin" and has a mass of m per unit area.  consider a small solid angle say around a 1 degree cone along the radius line.  Now as the shell is thin if the point is in contact with the inner area the small cone does not include any matter so the force is zero let us now move back a bit say far enough for the cone to intersect 1 unit area of mass m of the shell and that this distance is 1 unit of distance let us now look at the other side of the sphere.   If the distance to the other side is 1 unit we are in the centre and we know that the force is zero.  If it was 2 units of distance the cone would intersect (2 squared) 4 units of area of the shell (the area goes up as the square of the distance) and the gravitational force of the  4 units of mass will be reduced by 1/(2 squared) =  1/4  so the force exactly the same as the 1 unit of mass at 1 unit of length  So a net force of zero this applies whatever the size of the sphere because as the distance goes up and the force is reduced by the inverse square of the distance the mass in the little cone goes up as the square of the distance.

I hope that this is an adequate and simple enough proof.
« Last Edit: 29/07/2013 09:01:17 by Soul Surfer »
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Offline evan_au

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Re: How would gravity behave inside a hollow planet?
« Reply #34 on: 29/07/2013 10:05:42 »
At university, I also saw how Newton's law of gravity could be applied using calculus (also developed by Newton) to show that gravity is uniformly zero throughout a hollow shell.

Up to around the year 1900, it was thought that Newton's law of gravity adequately described the motion of bodies in our solar system. But, guided by Einstein's theory of relativity, we have now detected far more subtle gravitational effects close to the Sun that are better explained by Einstein than by Newton.

We know that Newton's theory becomes very inaccurate in the relativistic vicinity of a black hole. So if you wanted to test the hollow-shell theorem in a relativistic regime, you would pick a neutron star that was just short of becoming a black hole. You would then tunnel out a spherical cavity in the center, and repeat the hollow-shell experiment there.

We know that Newton's theory does not apply on cosmic scales (unlike Einstein's, which had his arbitrary cosmological constant, and today's dark energy theories). To test the hollow-shell theorem in a cosmological context, you would build a hollow-shell structure with the mass of a galactic cluster or more (but without it collapsing into a black hole!).

So while Newton's calculation would give you an answer that is extremely accurate on the scale of a hollow Earth, that does not necessarily extend to relativistic or cosmological environments.

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Re: How would gravity behave inside a hollow planet?
« Reply #35 on: 29/07/2013 13:44:51 »
Of course not!  But that was not the question.  This deals with a hollow planet.
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Re: How would gravity behave inside a hollow planet?
« Reply #36 on: 29/07/2013 16:14:15 »
Quote from: evan_au
Up to around the year 1900, it was thought that Newton's law of gravity adequately described the motion of bodies in our solar system. But, guided by Einstein's theory of relativity, we have now detected far more subtle gravitational effects close to the Sun that are better explained by Einstein than by Newton.
On that point I derived and expression for the inertial force on a particle in a gravitational field in a Schwarzschild spacetime (spacetime around a spherically symmetric distribution of matter in empty spacetime (i.e. matter is confined within a spherical region). The resulting force is velocity dependant as are all forces in relativity. If the body is falling radially inward or moving tangentially the force is the same and is given here

http://home.comcast.net/~peter.m.brown/gr/force_falling_particle.htm

I also derived this for the tangentially moving body and the result is the same. The result is

Gr = GMm(1 + v2/2)/r2

I find it delightful that here m is relativistic mass defined as m = P[sup0[/sup]/c = time component of 4-momentum (which is not always energy contary to popular belief). :)

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Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #37 on: 29/07/2013 19:48:23 »
Quote from: Bored chemist
For a certain definition of "easy".
Why is it beyond our engineering capabilities to fabricate a hollow shell of steel one meter thick with a radius of 20 meters? A an engineering feat that's easy by any definition in my humble opinion. It's measuring the gravitational field to high precision that's hard.

You seem to have forgotten what was originally written.
"I disagree. It's easy to create a hollow shell. Just get a small asterod and make it spherical and then hollow it out."
Which is odd, because you wrote it.
It would be fairly easy to make a steel sphere a foot across- they do it all the time.
A few tens of feet isn't a problem.
http://upload.wikimedia.org/wikipedia/commons/6/68/MiRO4.jpg

But none of those matter because it wouldn't be possible to measure the effect of the shell (especially when you are trying to prove that it isn't exactly zero).
You would need to reduce the effect of Earth's gravity for a start- so you would need to put it in orbit.

Are you beginning to see why this isn't actually "easy"?
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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #38 on: 29/07/2013 23:42:39 »
Quote from: Bored chemist
You seem to have forgotten what was originally written.
Whoops! Sorry my friend. :)
Quote from: Bored chemist
But none of those matter because it wouldn't be possible to measure the effect of the shell (especially when you are trying to prove that it isn't exactly zero).
You would need to reduce the effect of Earth's gravity for a start- so you would need to put it in orbit.
I had in mind the principle of superposition. The gravitational field in a region of space will remain unchanged when surrounded by a spherical shell. The gravitational field of the shell will have no effect on that field. This is one way to check the shell theorem if you first accept the principle of superposition.
Quote from: Bored chemist
Are you beginning to see why this isn't actually "easy"?
Nope. :)

I'm beginning to see how poorly I explained myself though. Does that count? LOL!!

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Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #39 on: 30/07/2013 20:58:51 »
It's tricky to speculate on how to measure something that we suspect doesn't exist.
Let's work out how easy it is to measure the effect of gravity directly- not the effect of surrounding a "meter" by a shell, but putting a big lump of mass above the "meter" and seeing how much difference it makes.
OK, a decent laboratory balance will resolve changes in weight of the order of a part in 100 million.
You can do a lot better with a gravimeter- but I'm not sure that counts as "easy": we can come back to it.

Now, I propose to put a big lump of stuff above the balance and see if I can measure the change in apparent weight.
How big a lump of stuff do I need?
Well, lets make a simple assumption- I will use "stuff" with about the same density as the Earth.

I will make the blob spherical- again, because it makes the maths easier.
Now, I can put the lump above the balance- the closest I can get it is the radius of the lump.
At that point it will attract the test object on the balance with a force which is proportional to the mass of the lump and inversely proportional to the distance from the centre of the lump.
The same applies to the gravitational attraction of the earth.
So if the lump of stuff is x times smaller than the earth then it will have an attraction x^3 times smaller, because it's less massive, but x^2 times bigger because it's nearer.
Overall, it will have an effect x times smaller than the earth.
If I want to spot that, it needs to be more than a hundred millionth of the attraction due to the earth.
So the lump needs to be no smaller than a hundred million times smaller than the earth.
The radius of the earth is roughly 6000000 metres so you need a lump of stuff that's at least 6,000,000 /100,000,000 metres. i.e. 6/100 metres that's only a few inches.

That looks so easy I'm sure I have made an error in the maths.

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Offline evan_au

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Re: How would gravity behave inside a hollow planet?
« Reply #40 on: 30/07/2013 22:41:16 »
Cavendish used 2" and 12" lead balls to estimate the strength of gravity, G.

But he mounted them in a horizontal plane, so he wasn't measuring small differences in Earth's attraction - but it was still a very tricky measurement.

See http://en.wikipedia.org/wiki/Cavendish_experiment

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Offline jeffreyH

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Re: How would gravity behave inside a hollow planet?
« Reply #41 on: 14/09/2013 03:14:30 »
Built your hollow sphere to a particular dimension and do a galileo. Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere. This method should apply to any earth bound hollow sphere no matter the size/mass.
Fixation on the Einstein papers is a good definition of OCD.

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #42 on: 14/09/2013 04:03:45 »
Quote from: jeffreyH
Built your hollow sphere to a particular dimension and do a galileo.
It's impractical to do so and since scientists don't question Newton's law of gravity nobody would build it.
Quote from: jeffreyH
Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere.
That makes no sense. That is not what physics predicts.

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Offline jeffreyH

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Re: How would gravity behave inside a hollow planet?
« Reply #43 on: 14/09/2013 04:26:08 »
Quote from: jeffreyH
Built your hollow sphere to a particular dimension and do a galileo.
It's impractical to do so and since scientists don't question Newton's law of gravity nobody would build it.
Quote from: jeffreyH
Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere.
That makes no sense. That is not what physics predicts.

So are you saying objects dropped from the same height under gravitation would fall at different rates?
Fixation on the Einstein papers is a good definition of OCD.

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #44 on: 14/09/2013 07:34:12 »
Quote from: jeffreyH
Built your hollow sphere to a particular dimension and do a galileo.
It's impractical to do so and since scientists don't question Newton's law of gravity nobody would build it.
Quote from: jeffreyH
Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere.
That makes no sense. That is not what physics predicts.

So are you saying objects dropped from the same height under gravitation would fall at different rates?
The subject of this thread is the question How would gravity behave inside a hollow planet?
which has been answered several times. There is no gravitational field inside a hollow planet. Therefore an object dropped from inside would move in the exact same way as if there was no planet at all, i.e. it wouldn't drop.

This has been explained over and over. Repeating and arguing about it will not change the answer. This is well known problem in gravitational physics and the answer is well known as well. The solution is calculated fairly easily. There is no mystery here. If you disagree with it then the problem lies in your education of physics, not the physics.

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Offline jeffreyH

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Re: How would gravity behave inside a hollow planet?
« Reply #45 on: 14/09/2013 18:43:51 »
The subject of this thread is the question How would gravity behave inside a hollow planet?
which has been answered several times. There is no gravitational field inside a hollow planet. Therefore an object dropped from inside would move in the exact same way as if there was no planet at all, i.e. it wouldn't drop.

This has been explained over and over. Repeating and arguing about it will not change the answer. This is well known problem in gravitational physics and the answer is well known as well. The solution is calculated fairly easily. There is no mystery here. If you disagree with it then the problem lies in your education of physics, not the physics.

My argument was to actually prove your point I wasn't arguing against you.
Fixation on the Einstein papers is a good definition of OCD.

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Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #46 on: 14/09/2013 21:02:51 »
The subject of this thread is the question How would gravity behave inside a hollow planet?
which has been answered several times. There is no gravitational field inside a hollow planet. Therefore an object dropped from inside would move in the exact same way as if there was no planet at all, i.e. it wouldn't drop.

This has been explained over and over. Repeating and arguing about it will not change the answer. This is well known problem in gravitational physics and the answer is well known as well. The solution is calculated fairly easily. There is no mystery here. If you disagree with it then the problem lies in your education of physics, not the physics.

My argument was to actually prove your point I wasn't arguing against you.
Oh. Okay. I actually only try to argue the point where the physics leads me. It's safer than way. :)