Journey to the center of the Earth

The higher you go the thinner the atmosphere, the lower the thicker the atmosphere. If you could build a pit to nearly the center of the Earth and had it insulated from the heat, would the atmospheric pressure alone crush you? And another thought, if you could build a sphere that was insulated and strong enough not to be crushed by the Earth, put it in the exact center of the Earth, then went inside, would you be weightless, pulled apart by the gravity, or kind just bounce from wall to wall?

The answer to the last question is you would be weightless. In fact, no matter how large the inner sphere or what position you are within it, you will be unaffected by the gravity from the outer sphere assuming the hollow sphere is a uniform thickness and density.

The notion that a body can be “crushed” by pressure is kind of a myth. Marine life of more or less normal composition is found in the deepest parts of the ocean (where pressure exceeds 1000 atm).

If you can’t be crushed, lets change the question a little, could you dig a deep enough hole on Mars where you’d have an atmosphere as dense as Earth? It wouldn’t be breathable but a simple scuba suit would be enough. And about being weightless no matter where you are in the sphere seems some how wrong to me, not saying it is. Lets imagine a neutron star. Give it a radius of 100 miles. Using my god-like powers I hollow out an interior sphere with a radius of 50 miles. Then using my god-like powers once again, I teleport 2 people inside. One in the center and one right near a wall. Wouldn’t the one near the wall be pulled to that wall since he’s closer to the center of gravity of that side of the neutron star? And if he’s pulled there wouldn’t the guy in the middle have different parts of his body closer to different walls and maybe pulled apart?

Well, using my Google Fu;

347 giga Pascals of pressure at the center of the earth!

Air pressure at the Earth’s surface is 101.3 kilopascals.

So the pressure at the center of the Earth, from the surrounding materials, is 3,425,469 times more than air pressure at the surface.

ETA: Oh, and that whole ‘can’t be crushed by pressure’ thing is absurd above certain values of pressure.

Rob Petrie: What is the main purpose in going to the Earth’s center?

Laura Petrie: To find out whether it’s chewy or chocolate creme.

This is the (estimated) actual pressure, based on mantle above, an iron-nickel core, etc. - it has nothing to do with the OP’s hypothetical.

Well, there’s gigapascals of pressure because the center of the EArth is solid iron.

In the OP’s scenario, we have constructed a cylinder, made of magical indestructible material, that extents from the surface to the center and is conveniently equipped with an elevator so you can ride all the way down. I do not have the math skills to figure out what the pressure would be at the center but it wouldn’t be 347 gigapascals.

As Ludovic points out, at the center of the Earth there would be no sense of gravity on either you or the air around you. The Earth’s gravitational force would be pulling at you in every direction at the same time, so you, and every air molecule, would be weightless. Atmospheric pressure in the biosphere is higher at sea level than stratospheric level becaudse there’s more air on top of you, and water pressure’s higher at the bottom of the Pacific than at the top for the same reason, but at any point we are talking about you are, basically, on the surface of the Earth; the gravitational difference between sitting on the beach or being at the top of Everest is insignificant. The depth of the ocean is equally insignificant in terms of determining the effect of gravity on pressure.

As you go down the elevator to hell, though, you will get deep enough that you’ll experience less gravitational pull towards the center of the planet. Fir the first while, air pressure will build up, because the effect of gravity will remain close enough to the same for government work and you’ll be under way more atmosphere. Again, I’m not smart enough to figure out how fast that happens or when you’d start noting it, but you and everything around you, including the air, will get lighter and lighter as you go, until finally you’ll “weigh” nothing at all.

I have a spreadsheet that models atmospheric pressure versus altitude. For each 100 feet up, it subtracts the pressure associated with that 100-foot layer, and calculates a new density for that new pressure. It also accounts for local atmospheric temperature (standard atmospheric temp profiles can be found on Google). The result is a curve: pressure drops off rapidly as you rise from sea level, but as you get to higher elevations, the pressure changes more slowly because each 100-foot layer contains less mass and so results in less reduction of pressure.

I ran the spreadsheet in the opposite direction, below sea level. I assumed a constant 68F. At the bottom of the Tautona mine in South Africa (2.4 miles below sea level), the atmospheric pressure is about 23 psi.

Just as atmospheric pressure drops off less and less rapidly at high altitudes, it drops off more and more rapidly as you go further down. However, one shortcoming of my model is that it doesn’t account for the reduction of gravity as you go deeper and deeper into the earth. This kind of doesn’t matter though, because pressures get stupid-high before you’ve gone deep enough for gravity reductions to matter. At just 200,000 feet of depth (38 miles), the atmospheric pressure would be 16,927 psi. You wouldn’t be “crushed”, since the solid/liquid parts of your body are essentially incompressible. But SCUBA divers can suffer from oxygen toxicity while breathing air at less than 100 psi, so you’d surely die before you get anywhere near the bottom of the hole.

The thing is, there’s a much bigger, although more remote part of the wall pulling in the opposite direction.

Actually, you can figure this out in your head without doing the triple integral. First, assume an “infinitely thin” spherical shell. Take any point inside the shell (call it P) and draw a random line through it. Let this line be the axis of a double cone of very small aperture, with the P at the apex. The intersections of this cone with the sphere will then be two similar ellipses, in opposite directions on the axis with respect to P, whose areas (and hence the mass elements they represent) are proportional to the squares of their distances from P. Now, you know that the gravitational pull from a mass element is proportional to its mass and inversely proportional to the square of the distance. So it follows that the net force on a particle in P will be zero in any direction!
For spheres with non-zero thickness, just imagine them composed of infinitely many infinitely thin layers…

Does that mean if you built a perfect Dyson sphere around a star, the people on the interior surface would be weightless? Or would it be even worse since you would have a gravity source in the center (the srar)? Would they actually be pulled away from the interior surface?

The gravitational field inside a Dyson sphere would be exactly the same as it would be without the sphere, i.e., the gravity of the star inside.

It almost doesn’t matter at all. If the Earth were a sphere or uniform density, then the gravitational field strength would decrease linearly as you went from 9.8 m/s^2 at the surface to 0 at the center. But the Earth isn’t uniform: Its density tends to increase as you get deeper. In fact, it does it in just such a way that the gravitational field strength remains approximately constant all the way from the surface to the edge of the core, and then decreases more or less linearly from there. I’m not sure if this is a coincidence, or if it reflects some material property of the minerals that make up the Earth.

Moved to GQ.

A previous incarnation of this question: “Air pressure at the centre of the Earth. (In a hole.)” from 2006

I’ll go with metric buttloads … seems a reasonable amount … ummm … the human body has a few cavities, some are actually really important, these would be crushed with 100’s of GPa’s

Huh. I read this thread thinking, “That’s an interesting question”, and it turns out I already asked it, 10 years ago. :smack:

That will come as a surprise to a few submarine crews.

But that life spends all its existence at that pressure, so its internal pressure is the same. It’s not pressure per se that will crush you, it’s pressure inequality.

Are you suggesting that excessive hydrostatic pressure is the cause of death for the crews of imploded submarines, rather than drowning or blunt-force trauma from objects accelerated to high speed by the implosion event?

How do you imagine the sudden application of high hydrostatic pressure causes death?

No, I didn’t suggest that. If a submarine implodes on you then you have more… uh… pressing issues than the water pressure.

That said, sudden changes in pressure are bad news if you are diving. If you gradually acclimatise, and have suitable arrangements to breathe, then you can withstand huge pressures. Going suddenly from ~1atm to deep underwater would not be a good thing.

Apart from potentially rupturing eardrums, in what way is a sudden large pressure increase bad for you?