center of earth thought experiments

[billwald]

Gravity is a very weak force. The mass on the entire earth acting on me only produces a force of approx. 220 pounds (the force of my mass acting on the earth is insignificant). Right?

Say there was a (1 foot dia) titanium sphere at the center of the earth. It is said that the pressure at the center of the earth is caused by gravity. How could the force of gravity on the sphere be very much larger than the force of gravity on me?

Say the earth is solid, no liquid core. Say it is cut into rigid hemispheres with sufficient strength to maintain the hemispheres. Say we seperate the halves with strain gauges. How much pressure will be noted on the gauges?

 

[Mathematician]

Gravity is a very weak force. The mass on the entire earth acting on me only produces a force of approx. 220 pounds (the force of my mass acting on the earth is insignificant). Right?

Say there was a (1 foot dia) titanium sphere at the center of the earth. It is said that the pressure at the center of the earth is caused by gravity. How could the force of gravity on the sphere be very much larger than the force of gravity on me?

Say the earth is solid, no liquid core. Say it is cut into rigid hemispheres with sufficient strength to maintain the hemispheres. Say we seperate the halves with strain gauges. How much pressure will be noted on the gauges?

The gravitational force at the center of the earth is zero.

 

[DaveS]

I thought the center of the Earth (that is actual center) was solid?

Gravity is a thing that I do not even try to understand! How can we predict a force that we do not even know the cause of or how it does it? All we know is that it seems to be relative to the density of something, maybe mass, maybe not.

 

[ebia]

I thought the center of the Earth (that is actual center) was solid?

It doesn't matter - the only gravitational effect is from the stuff that is closer to the centre than you are. Everything that is further away cancels each other out (assuming that the earth is spherical).

Gravity is a thing that I do not even try to understand! How can we predict a force that we do not even know the cause of or how it does it?

We look at what effect it has. We theorise that the force is proportional to the mass, and inversely proportional to the square of the distance. And we find out that works in every case we examine.

 

[LewisWildermuth]

Gravity is a very weak force. The mass on the entire earth acting on me only produces a force of approx. 220 pounds (the force of my mass acting on the earth is insignificant). Right?

Say there was a (1 foot dia) titanium sphere at the center of the earth. It is said that the pressure at the center of the earth is caused by gravity. How could the force of gravity on the sphere be very much larger than the force of gravity on me?



Say the earth is solid, no liquid core. Say it is cut into rigid hemispheres with sufficient strength to maintain the hemispheres. Say we seperate the halves with strain gauges. How much pressure will be noted on the gauges?

The force of gravity is just the start of the cause of the pressure, it just gives things weight, the pressure at the center of the Earth is higher than it would be just taking simple gravity in account because of the combined weight of all the things above you. Just like walking down a mountain or diving deeper into water, the pressure goes up quite quickly even though you could not notice the change in gravity.



As far as the separating force, to calculate that you need the weight of the half of the Earth you are trying to move and the energy it would take to get that mass moving at escape velocity... Let me see if I can get some numbers...

 

[KnowBeDo]

42

 

[billwald]

>diving deeper into water, the pressure goes up quite quickly even though you could not notice the change in gravity

Interesting. I'll have to think about it.

Say one drilled a hole to the center of the moon and set off a very large nuke. It would create a large hole with no noticable gravity? If one could create a small black hole at the center then the moon would self-center itself around the black hole. It could be used as a power generator?

 

[ebia]

>diving deeper into water, the pressure goes up quite quickly even though you could not notice the change in gravity

Interesting. I'll have to think about it.

Say one drilled a hole to the center of the moon and set off a very large nuke. It would create a large hole with no noticable gravity?

So you create a spherical chamber centered on the centre of the moon? Then that is correct, there would be no gravity (from the moon) inside that chamber.

If one could create a small black hole at the center then the moon would self-center itself around the black hole.

Um, no.

 

[LewisWildermuth]

Say one drilled a hole to the center of the moon and set off a very large nuke. It would create a large hole with no noticable gravity?

Not with the process you stated... It is quite a bit more complex than that. If, for simplicities sake, we had a perfectly smooth moon with no wobble and it was perfectly consistent in material from crust to core and the gravity of everything else in the universe did not affect it (all of which are not our Moon), then if you made a perfectly spherical void in the center you could suspend a perfect sphere in the exact center of that void because gravitational pull from the walls would perfectly counteract each other in the center. It would look like there was no gravity and the object was just floating but in fact it would just be being pulled from all sides evenly.

If one could create a small black hole at the center then the moon would self-center itself around the black hole. It could be used as a power generator?

Not in reality, maybe in sci-fi, but to create a black hole would take tons of energy, to balance it in the center and keep it from eating anything more, and unless it eats things I know of no theoretical way to harvest energy from one.

 

[LewisWildermuth]

I am not a physics expert, if anyone wants to step in and correct anything I have said, feel free, I always look forward to a better understanding in any subject.

 

[Mathematician]

Tiny correction,

If ... we had a perfectly smooth moon with no wobble and it was perfectly consistent in material from crust to core and the gravity of everything else in the universe did not affect it (all of which are not our Moon), then if you made a perfectly spherical void in the center you could suspend

anything you want anywhere in

that void because gravitational pull from the walls would perfectly counteract each other in the center. It would look like there was no gravity and the object was just floating but in fact it would just be being pulled from all sides evenly.

Not in reality, maybe in sci-fi, but to create a black hole would take tons of energy, to balance it in the center and keep it from eating anything more, and unless it eats things I know of no theoretical way to harvest energy from one.

The black hole would strip stuff from the outside of the void and make the moon collapse.

 

[LewisWildermuth]

Tiny correction,
anything you want anywhere in

Thinking about it, yes you could balance anything, but since the walls of the void would still be pulling things toward themselves, would it not have to be in the exact center?

The black hole would strip stuff from the outside of the void and make the moon collapse.

Yes, I may have not been as clear as I had intended. You would have to expend energy to keep the moon from being pulled into the black hole. Once material is pulled from one side or another then the balance would collapse. Or if you were to feed the black hole somehow without upsetting the balance (I am not sure how you would do this) the energy released as the "food" approached the black hose could upset the balance and act as a rocket, moving the black hoe off center.

 

[ebia]

Not with the process you stated... It is quite a bit more complex than that. If, for simplicities sake, we had a perfectly smooth moon with no wobble and it was perfectly consistent in material from crust to core and the gravity of everything else in the universe did not affect it (all of which are not our Moon), then if you made a perfectly spherical void in the center you could suspend a perfect sphere in the exact center of that void because gravitational pull from the walls would perfectly counteract each other in the center. It would look like there was no gravity and the object was just floating but in fact it would just be being pulled from all sides evenly.

Just to clarify though, there would be nothing actually keeping the system centred - if anything were slightly off or something disturbed the system (eg an impact on the outside of the moon) then the system would drift off centre until the 'black hole' hit the side. It's not a stable system.

 

[LewisWildermuth]

Just to clarify though, there would be nothing actually keeping the system centred - if anything were slightly off or something disturbed the system (eg an impact on the outside of the moon) then the system would drift off centre until the 'black hole' hit the side. It's not a stable system.

Yes, I agree, it would be like trying to balance a semi on the point of a pin in a tornado. Maybe not imposible with unlimited energy and technology, but not easy and kinda pointless.

 

[Mathematician]

Thinking about it, yes you could balance anything, but since the walls of the void would still be pulling things toward themselves, would it not have to be in the exact center?

No, it's a standard freshman physics problem. Assume the earth is a perfect spherical shell. If the object is off center, there's more stuff pulling on the far side,. But it's father away. It exactly cancels.

 

[LewisWildermuth]

No, it's a standard freshman physics problem. Assume the earth is a perfect spherical shell. If the object is off center, there's more stuff pulling on the far side,. But it's father away. It exactly cancels.

Physics was not required at my old high school (and rarely offered), so I had to teach myself. :o



But I was thinking in terms of the power of gravity being an inverse square to the distance... Wouldn’t drifting too close to one of the walls eventually overpower the draw from the other areas?

 

[ebia]

Physics was not required at my old high school (and rarely offered), so I had to teach myself. :o



But I was thinking in terms of the power of gravity being an inverse square to the distance... Wouldn’t drifting too close to one of the walls eventually overpower the draw from the other areas?

Assuming the moon is spherical, the chamber is spherical, and they have the same centre, then no.

I don't much fancy the idea of dredging up the maths to prove it, but the answer is definitely no.

 

[Mathematician]

But I was thinking in terms of the power of gravity being an inverse square to the distance... Wouldn’t drifting too close to one of the walls eventually overpower the draw from the other areas?

HS physics won't do it. The proof requires calculus. The closer you get to one side, the more stuff on the other side to pull. It balances out.

I'll try to do a picture for you.

Draw a circle on a piece of paper. Draw a dot precisely in the center. Draw two lines through the center resembling a squished X. Notice that the arc on each side is the same length.

Do this again, except place the dot near one side. Measure the distance from the point to the center of the arc on each side. Measure the length of the arc. For all arcs, arc length divided by distance to center of arc is the same on both sides of the x.

That arc length on the circle represents a circle on the surface of the sphere. That is, an area or squared length. This precisely cancels the inverse square for gravity.

See also http://www-spof.gsfc.nasa.gov/stargaze/StarFAQ2.htm#q29

http://www.merlyn.demon.co.uk/gravity1.htm#GoSSh

http://www.merlyn.demon.co.uk/gravity1.htm#GoSp

 

[LewisWildermuth]

I understand that the gravity well of the void would balance itself out, but any object placed in that void would have its own gravity well. That is what I thought would throw the balance off.



I’ll have to do some calculations when I get the time... Thanks for the help

 

[Mathematician]

I understand that the gravity well of the void would balance itself out, but any object placed in that void would have its own gravity well. That is what I thought would throw the balance off.

Only if it distorts the shape of the perfect spherical shell.