At Center of Earth: Weightless or Crushed?

[Cyrus]

I know that if you are in the center of the earth, gravity will act on you equally in all directions so you will feel weightless. But at the same time, won't you be crushed to death? Since you have the pressure of all that mass around you in all directions? It would seem that being weightless would be the least of your problems.

 

[mathman]

It depends on whether or not you can create a cavity at the center so you won't be crushed. Actually, the center of the Earth is molten iron, so you would be cooked if you didn't do anything.

 

[Nenad]

I know that if you are in the center of the earth, gravity will act on you equally in all directions so you will feel weightless. But at the same time, won't you be crushed to death? Since you have the pressure of all that mass around you in all directions? It would seem that being weightless would be the least of your problems.

Well actually, no you won't. Because think about a rock that is 10m away from the centre, it too has an environment of extremely low gravity on it, sonce there is tons of Earth pulling it in all directions. This is why the centre of the Earth is composed of a very fluid (non dence) material, because the gravity is so low.

The best way to look at gravity when digging in the Earth is to do it ilke this. Let's say you are 1000m beneath the earth, the pull of gravity on you now is:

F_g = \frac{GM_{1} M_{2}}{(r - 1000m)^2}

I am assuming that the loss of mass from that 1000m less is neglegable but you can think of it this way. So the deeper you go down, is like decreasing the radius of your planet, so if you are 10m from the centre, the force of gravity on you would be the size of a force you would experience on a 10m radius planet, or barely nothing. If you don't understand, ask away?

 

[Hurkyl]

When you're deep under the crust, it's not the gravity you need to worry about, it's the weight of all of the stuff above you.

 

[Cyrus]

Well actually, no you won't. Because think about a rock that is 10m away from the centre, it too has an environment of extremely low gravity on it, sonce there is tons of Earth pulling it in all directions. This is why the centre of the Earth is composed of a very fluid (non dence) material, because the gravity is so low.

The best way to look at gravity when digging in the Earth is to do it ilke this. Let's say you are 1000m beneath the earth, the pull of gravity on you now is:

F_g = \frac{GM_{1} M_{2}}{(r - 1000m)^2}

I am assuming that the loss of mass from that 1000m less is neglegable but you can think of it this way. So the deeper you go down, is like decreasing the radius of your planet, so if you are 10m from the centre, the force of gravity on you would be the size of a force you would experience on a 10m radius planet, or barely nothing. If you don't understand, ask away?

How would you not experience the weight of all the Earth above you. You would not feel its gravity, but you would feel its weight. If i bury you alive, you surely will feel the weight of all that soil around you. In fact, you would hardly be able to dig your way out. Just like a person in an avalanche is unable to dig himself out of a couple feet of snow. I thought the reason for the molten core is the extreeme pressure of all the earth. All that preassure equals tons and tons of heat. Heat which can thereby liqify the core, and thus the magma. Its just like hydrostatic pressure, it will increase with depth. As you go deeper, all the weight of the water above you will pile up. At the core of the earth, you have the weight not only pushing you down, but side ways too, trying to swash you in all directions, as opposed to just down when your relativly deep in the earth. Here is a neat proof of what I am talking about.
http://burro.astr.cwru.edu/Academics/Astr221/SolarSys/hydrostat.html as you can see, the pressure at the center of the Earth is clearly not zero, but very very very great. You would be hard pressed to disprove me

 

[Nenad]

read my post again, and notice the key words I am talking about 'gravity' and NOT 'pressure'. And you can't compare something like an avalanche or being burried in the Earth's crust to the centre of the earth. If you think about it, if you are 5m from the cnetre, you will not feel great weight of soil because that soil is being pulled in all directions, just like you are, cancelling out gravity, and therefore cancelling out pressure. The centre of the Earth is way different that the ouside shell.

 

[Tide]

Near the center of the Earth the gradient of the pressure will tend toward zero because the gravitational force tends toward zero. That does not mean, however, that the pressure is zero! In fact, the pressure will be proportional to the mass of the entire planet.

 

[Brad Barker]

wouldn't the gravity tend towards infinity?

 

[elas]

Surely you are overlooking the major difference between Newton's gravity and Einsteins gravity, the last time I read anything on this difference it was that the force direction was unknown and still subject to debate.

 

[Hurkyl]

Consider this, Nenad:

Get two equally strong friends, have one stand in front of you, and one stand behind you. On your mark, have them both start pushing you with all their might.

The net force you feel will be zero, since you're being pushed with equal force from in front and behind... but that doesn't stop you from being crushed in the process.

 

[Hurkyl]

wouldn't the gravity tend towards infinity?

No. Inside a uniformly dense spherical object, gravity dies off linearly... the gravity you feel is directly proportional to your distance from the center.

 

[Doc Al]

Just to add to Hurkyl's comments: The pressure on you at the center of the Earth is not due to the gravitational attraction between you and the earth--that tends to zero. The crushing pressure is due to the gravitational attraction of the Earth with itself--the force holding the Earth together. You are just crushed in the middle.

 

[GOD__AM]

Consider this, Nenad:

Get two equally strong friends, have one stand in front of you, and one stand behind you. On your mark, have them both start pushing you with all their might.

The net force you feel will be zero, since you're being pushed with equal force from in front and behind... but that doesn't stop you from being crushed in the process.

The differnece between this anology and the reality of being burried in the Earth is that the pressure is not applied evenly in your example. When pressure is exerted evenly, such as when imersed in water the human body can take a lot of crushing force without noticing at all. Granted the pressure and tempature at the center of the Earth would pulverize us.

 

[Cyrus]

read my post again, and notice the key words I am talking about 'gravity' and NOT 'pressure'. And you can't compare something like an avalanche or being burried in the Earth's crust to the centre of the earth. If you think about it, if you are 5m from the cnetre, you will not feel great weight of soil because that soil is being pulled in all directions, just like you are, cancelling out gravity, and therefore cancelling out pressure. The centre of the Earth is way different that the ouside shell.

If I bury you under 5 feet of soil, you will feel its weight, I assure you. In fact, you will feel the integral of the gravity as it starts from 9.81 m/s/s at the surface time that point mass, all the way down until you reach the center. So you will infact feel the sum of all these gravitational forces added together and you will feel a lot of pressure and force. You just won't feel any gravitational force. But I think we are debating the same point of view.

 

[mathman]

When pressure is exerted evenly, such as when imersed in water the human body can take a lot of crushing force without noticing at all.

Not true. If a submarine dives too deeply it will be crushed.

 

[GOD__AM]

Not true. If a submarine dives too deeply it will be crushed.

Read what I typed. "The human body" not a submarine is what I said. The human body is made of mostly water, as most of us know, and as a result is largely uncompressable. The submarine would never crush if the air pressure inside was equal to the water pressure outside, which is how divers breathe underwater.

 

[chroot]

read my post again, and notice the key words I am talking about 'gravity' and NOT 'pressure'. And you can't compare something like an avalanche or being burried in the Earth's crust to the centre of the earth. If you think about it, if you are 5m from the cnetre, you will not feel great weight of soil because that soil is being pulled in all directions, just like you are, cancelling out gravity, and therefore cancelling out pressure. The centre of the Earth is way different that the ouside shell.

This is pretty much entirely false. The condition of hydrostatic equilibrium requires that the pressure at the center of the Earth be higher than at the surface. In fact, the pressure is very intense there. Please refrain from making comments about physics you have yet to learn properly.

- Warren

 

[Cyrus]

Hey he was only trying to help warren. He did infact help me on another problem, so its cool if he made a simple mistake. At least we will both learn in the process, and that is the whole point of this forum anyways.

 

[geometer]

The differnece between this anology and the reality of being burried in the Earth is that the pressure is not applied evenly in your example. When pressure is exerted evenly, such as when imersed in water the human body can take a lot of crushing force without noticing at all. Granted the pressure and tempature at the center of the Earth would pulverize us.

It's not whether the pressure is applied evenly, it's actually not the pressure itself, it's the pressure differential between the inside of your body and the outside, and the material strength of your body. The reason a submarine gets crushed at a certain depth is that the pressure inside the boat is about atmospheric and the pressure outside is thousands of pounds per square inch. If the pressure inside the boat were always the same inside as outside, it would never be crushed.

 

[GOD__AM]

It's not whether the pressure is applied evenly, it's actually not the pressure itself, it's the pressure differential between the inside of your body and the outside, and the material strength of your body.

Ok, an example; The Navy conducts saturation dives at depths over 2000 feet in the ocean. This is equal to about 1000 psi of pressure (as opposed to the 14.7 psi we are exposed to typically). Applied evenly btw, and the divers surely aren't crushed or even aware of any extra pressure they feel. Take the same person, lie them down on the Earth and put a 1000 lb concrete slab on them. What happens next is the person splits at the sides where the pressure is uneven.

The reason a submarine gets crushed at a certain depth is that the pressure inside the boat is about atmospheric and the pressure outside is thousands of pounds per square inch. If the pressure inside the boat were always the same inside as outside, it would never be crushed.

This is pretty much what I said in my second post and I agree. There should be a point where bones and other non-liquid parts of the body will succumb to the pressure, but I'm not sure how much it would take.

 

[Nenad]

This is pretty much entirely false. The condition of hydrostatic equilibrium requires that the pressure at the center of the Earth be higher than at the surface. In fact, the pressure is very intense there. Please refrain from making comments about physics you have yet to learn properly.

- Warren

I don't know it you have fun proving 17year old kids wrong, but a mistake is a mistake. My vector addition was wrong, and I missed something. I hope you feel satisfied. Later.

 

[geometer]

Ok, an example; The Navy conducts saturation dives at depths over 2000 feet in the ocean. This is equal to about 1000 psi of pressure (as opposed to the 14.7 psi we are exposed to typically). Applied evenly btw, and the divers surely aren't crushed or even aware of any extra pressure they feel. Take the same person, lie them down on the Earth and put a 1000 lb concrete slab on them. What happens next is the person splits at the sides where the pressure is uneven.

Wow - is this true?! I spent 13 years in the Navy, and I don't remember any dives this deep!

 

[geometer]

Ok, an example; The Navy conducts saturation dives at depths over 2000 feet in the ocean. This is equal to about 1000 psi of pressure (as opposed to the 14.7 psi we are exposed to typically). Applied evenly btw, and the divers surely aren't crushed or even aware of any extra pressure they feel. Take the same person, lie them down on the Earth and put a 1000 lb concrete slab on them. What happens next is the person splits at the sides where the pressure is uneven.

After doing some quick reading on saturation diving, I find it is true! To do this, the divers raise the partial pressure of gases in their system to that of the depth they are operating at - in other words, they reduce the differential pressure between their insides and their outsides to zero.

 

[Cyrus]

I find this hard to belive. I think 1000psi inside the cabin of a sub would be terrific forces in all directions. I would think a persons ears would pop not to mention their body being crushed like a tin can. Its true the pressure in and out of the sub are about equal, but to a person inside the sub, isint he going to feel 1000psi pressure relative to inside the cabin? It would seem only insturments could servive that pressure, and big bulky ones at that.

 

[GOD__AM]

I find this hard to belive. I think 1000psi inside the cabin of a sub would be terrific forces in all directions. I would think a persons ears would pop not to mention their body being crushed like a tin can. Its true the pressure in and out of the sub are about equal, but to a person inside the sub, isint he going to feel 1000psi pressure relative to inside the cabin? It would seem only insturments could servive that pressure, and big bulky ones at that.

First off a submarine is not pressurized any different than on the surface, 14.7 psi. That is why they have to be so strong, to hold out the pressure.

Secondly in diving compressed gas is used and supplied through a regulator that supplies air in relative density to the water pressure around it(typical hi pressure scuba tanks hold about 3500psi or more). A diver then has to force air into his inner ear to "equalize" the pressure as he descends deeper. This is done for most by pinching the nose with the mouth closed and forcing the pressure into the ear canal. During ascent the equalizing occurs naturally as long as the ascent rate isn't too fast.

On a final note you say the people in the sub should feel the pressure (if it were pressurized). Well hypobaric chambers used in medacine and treatment and study of the effects of pressure on the body do just this. They actually pump compressed air into the chamber with the people in it. Other than some slight heating during the compression and the necessity to "equalize" the inner ear, there is no sensation of being compressed.

 

[geometer]

I find this hard to belive. I think 1000psi inside the cabin of a sub would be terrific forces in all directions. I would think a persons ears would pop not to mention their body being crushed like a tin can. Its true the pressure in and out of the sub are about equal, but to a person inside the sub, isint he going to feel 1000psi pressure relative to inside the cabin? It would seem only insturments could servive that pressure, and big bulky ones at that.

You don't feel pressure, you feel differential pressure. If the pressure of the gases inside your body is 1000 psi, and the pressure outside is 1000 psi, you will feel nothing. This is the trick in saturation diving - take the time to slowly and carefully equalize your "internal" pressure with the external pressure, and it would be just like you were sitting in your living room watching TV.

 

[Cyrus]

Hmm weard. Can you acutually go to 1000psi though? That seems wayyyyy wayyy too hight :-) I would think even 100psi on the body would be pusshing it. Thats nearly 1470 lbs per square inch on a human body. ouch.

 

[GOD__AM]

Hmm weard. Can you acutually go to 1000psi though? That seems wayyyyy wayyy too hight :-) I would think even 100psi on the body would be pusshing it. Thats nearly 1470 lbs per square inch on a human body. ouch.

Yes, as I said in a post you quoted, the navy has done dives at these high pressures. You seem to be missing the fact that the human body is mostly water and is uncompressable. Only the air spaces in our body will compress. Oh and your math is flawed. 100 psi on the body = 100 lbs per square inch not 1470.

Just consider this if you are having trouble with the idea. Animals live very deep in the ocean, possibly even in the deepest trenches there is life. Whales dive very deep, and they don't even have the benifit of breathing compressed gas to offset the pressure. So effectively the air spaces in their bodys are crushed proportional to the pressure of the water acting on them, yet they suffer no ill effects.

One more thing that may help you. If I take a plastic bag and fill it with water, then throw it off a boat into the deepest part of the ocean, as the bag decends into more and more pressure it still occupys the same amount of space or volume as it did on the surface. There is no compression.

 

[geometer]

Yes, as I said in a post you quoted, the navy has done dives at these high pressures. You seem to be missing the fact that the human body is mostly water and is uncompressable. Only the air spaces in our body will compress.

I think this is a little misleading. The water in the human body is incompressable, but the human body itself is eminently compressable. The water in our bodies is contained within cell walls which certainly can rupture and leak all this water out. As an example (rather gruesome I admit), think of what happens to an animal that has been repeatedly run over on the road; it gets very flat! As kids we used to refer these as "sail cats, or sail whatever animal." You could pry them up and use them like frisbees.

Theoretically, I suppose you could exist under any pressure, if there was no differential across your body. I am sure there are physiological and structural limits to this, but the trick behind saturation diving is to raise the partial pressures of the gases in the human body to the pressure of the depth you will be diving at - 0 delta P means 0 problems.

 

[Cyrus]

My mistake God_AM, I meant to say 100atm not 100psi. 100atm would be 1470 psi, my fault. I made a NASA units conversion mistake. ;-P