Question: if you dug a whole right through the middle of the earth and went in the middle would you fall through or stay in the middle.
Comments
-
My wife, who is South African, wanted me to point out that they have the deepest mines in the world there:
http://news.nationalgeographic.com/news/2007/11/071106-africa-mine.html
and that even at depths of a few kilometers, the temperature gets unpleasantly high. Think about that – a few kilometers. What’s the radius of the Earth? Over 6000 kilometers! So at less than 0.1% of the way to the core, things are difficult. Imagine what it’s like when you get really deep.
Still thinking about the pressure thing though. Assuming you’ve got a tunnel – a perfect tunnel with very strong heat-resistant walls. It runs from your school (let’s pretend) to the centre of the earth. So 6000 kilometers. And it’s open to the air (not closed at the top). And assume that the temperature is kept at room temperature all the way down using a truly awesome air conditioning unit you add in. Question: What’s the pressure at the end of the tunnel (at the centre of the earth)?
I think that’s a difficult maths problem. But I think that when you work it out, it’ll be A LOT. Let me ask around.
-
Hi Matt,
Yes, the pressure would be a lot, but not QUITE as much as you might think because you have to remember that the gravitational field strength will decrease proportional to r inside the earth (where r is the distance to the centre). So, assuming that air is incompressible, you just integrate the weight (per unit area) along (half) the column: \int_{0}^{R} \rho (g/R) r dr, where R is the radius of the Earth, g the gravitational field strength (acceleration) at the Earth’s surface, and \rho the density of air, and add the integral to the air pressure at the Earth’s surface.
The pressure at the centre is therefore 1 atmosphere + (1/2) \rho g R. Plugging in the numbers, this is 1atm + (1/2) * 1.2 kgm^{-3} * 9.8 ms^{-2} * 6.37*10^{6}m = 1atm + 3.12 x 10^{7} Pa = 309 atm. So yes, a LOT of pressure!
-
Aimee, Mat, dilligaf,
No, you would NOT stop at the centre: unless you travelled down there very slowly.
If you jumped in from the top of the hole, you would go right to the other side of the Earth, and then fall back through to the original side, and then back again, and so on for ever and ever (if it wasn’t for drag from the air slowing you down).
Matt and Aimee, because gravity is proportional to r inside the earth, in the absence of air drag you would just move from one end of the hole to the other and back again in simple harmonic motion.
-
Edward – definitely. I was assuming you could “go” there and stop, then wait. If you did the crazy thing which is TO JUMP IN THE FIREY HOLE OF DOOM then yes, you’d zoom in and out to nearly the surface of the earth the other side. Most unamusing, but presumably very funny to people watching. You’d get respect from a lot of the caving community.
Awesome calculation. That’s a lot of pressure. If the air is compressible it gets worse, right? Because there’s actually more stuff above you at the bottom? But if you factor in heat it’s less bad (from the pressure point of view).
-
Hi Mat, both those sound right to me: but I couldn’t do the calculation without doing some serious swatting up on fluid dynamics!
-
-
A guy called Neil Saunders at CSIRO in Sydney just passed this along:
http://www.freemaptools.com/tunnel-to-other-side-of-the-earth.htm
Allows you to work out where your tunnel would come out on the other side of the Earth, if you went all the way through! 🙂
Looks like if you dig from Australia you’d come out in the really deep trench that’s in the middle of the Atlantic. Shorter tunnel. Very watery at the other side.
-
Nifty little app! 😀
-
Edward
That’s a clever question dilligaf.
At the moment we can dig a hole a couple of thousand metres deep. But compared to the size of the Earth, that’s just like digging through the orange bit of an orange skin. Not even into the pithy bit.
If we could dig a deeper hole we would get through to the rocky mantle then the molten core. This far down into the Earth there would be so much heat and so much pressure that we would probably be squished into a burning little ball.
We can ignore all that though and pretend that we can dig a hole like that and survive the journey through it. So, would we fall out the other side of the Earth, or would gravity keep us in the middle?
My vote is that gravity would cancel out at some point in the middle and we would get stuck there. I don’t think we would just come to a gentle stop and float around there though, I think that the force of gravity from each side (and right near the middle it should be even stronger than the gravity up here at the surface) would crush us into a tiny little ball.
So I think crushed and burnt is the only option if we go burrowing.
0
You’d stay in the middle. Gravity pulls you towards stuff. We feel a downward force because the earth is under our feet. If you were in the middle, all the forces would cancel out and you’d sit there.
But yes, it’s kind of hot down there, because of all the temperature and pressure.
Interesting question, though – if you dug a tunnel then it’d be crushed by the pressure of everything pulling towards everything else. But if you imagine for a second that you could build a tunnel that was super-strong – strong enough to withstand the forces of the earth above you, then what?
That’s a good question. I think the air pressure would still be intense down there, even if the tunnel holds the rock and heat back. In effect you’d have a column of air thousands of miles high pressing down on you. That’s probably not what you want. At the centre, everything would cancel and you wouldn’t be pushed anywhere because the air wouldn’t be moving, but the pressure would still squash you pretty badly.
0
The main problem as Aimee and Matt have indicated is that the centre of the earth is hot — so hot that all the rocks have melted, essentially magma or lava.
But let’s imagine that somehow a tunnel was built the whole way through and it was air-conditioned to be cool and so on. So we jump into the hole — the vertical tunnel. There is a thing called terminal velocity. Air friction slows falling bodies so that they have a maximum (terminal) speed (velocity). That’s why raindrops falling from a few kilometers up don’t kill us. The air friction means that the raindrops never do faster than some terminal velocity. So now we are falling down this hole. The air friction means that we’d never go faster than our terminal velocity. This means we do not go fast enough to shot all the way up the other half of the tunnel. This slowing effect by air friction is why a swing does not quite goes as high as it started.
So yes, we’d get stuck in the middle, and eventually die. 🙁
So lets get rid of the air friction by pumping all the art out and having a vacuum. Now, we’d keep accelerating all the way down to the centre of the earth and shot all the way up the far side. But with no air, we’d die … we’d come out but not alive. 🙁
So lets go through the tunnel in a vacuum wearing a space suit. I haven’t worked out the physics and maths but it would would take hours or perhaps days to fall all the way though … so we’d run out of air and die. 🙁
Lets build bigger spacesuit. Big enough to survive a few days. Well after all this effort, it would be cheaper and easier to fly on that hypersonic jet that burns fuel from seaweed. 🙂 What? It would take too long to design and build the hypersonic jet? It would be built and finished heaps faster than our tunnel though the centre of the earth!
0