Center of the Earth

1. Sep 1, 2004

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, wont 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.

2. Sep 1, 2004

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.

3. Sep 1, 2004

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. Lets 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 dont understand, ask away?

4. Sep 1, 2004

Hurkyl

Staff Emeritus
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.

5. Sep 1, 2004

Cyrus

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 :rofl:

Last edited: Sep 1, 2004
6. Sep 2, 2004

read my post again, and notice the key words I am talking about 'gravity' and NOT 'pressure'. And you cant compare something like an avalanche or being burried in the earths 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.

7. Sep 2, 2004

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.

8. Sep 2, 2004

wouldn't the gravity tend towards infinity?

9. Sep 2, 2004

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.

10. Sep 2, 2004

Hurkyl

Staff Emeritus

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. :tongue:

11. Sep 2, 2004

Hurkyl

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

12. Sep 2, 2004

Staff: Mentor

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.

13. Sep 2, 2004

GOD__AM

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.

14. Sep 2, 2004

Cyrus

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 alot of pressure and force. You just wont feel any gravitational force. But I think we are debating the same point of view.

15. Sep 3, 2004

mathman

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

16. Sep 3, 2004

GOD__AM

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.

17. Sep 3, 2004

chroot

Staff Emeritus
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

18. Sep 3, 2004

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.

19. Sep 3, 2004

geometer

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.

20. Sep 3, 2004

GOD__AM

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.

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.