Have you ever asked yourself what would happen if you drill a hole into the earth's s

sepa0202

Hi guys,

(Have you ever asked yourself what would happen if you drill a hole into the earth's surface that reaches to the other end of the planet and then jump in?)

It's a question that many pupils have asked me already. I bet you've thought about it at least once in your life...
I asked them that question, and there were silly but ingenious answers such as "once you've reached the other side of the earth's crust, you go into space, like a rocket..." or "you get trapped in the middle of the earth".
The second one is not so silly though, but it's still not like that.
I am going to explain, for those who don't know, what would happen in the hypothetical case if you drill or dig a hole which reaches to the other end of the planet.
Okay, it seems quite stupid, because you get burned for sure... But let's imagine that we are wearing special and fireproof suits and it's possible to do it.

So, okay, we've drilled the hole. Now it's the time to jump in, and start to accelerate.
You would accelerate at 9.8 m/s to a velocity of around 38.000 km/h, or 22.000 miles per hour. That's a hell of a lot.
Anyway, once you've reached the centre of the earth, you will start decelerating, because gravity will act on you on the oppposite direction. And just when you reach the earth's surface, your velocity would be 0. So there should be someone to pick you. If nobody grabs you, you will fall again....
By the way, it takes you 42 minutes exactly to reach the other side of the earth.
Eventually, and it might take you ages, you will end up trapped on the centre of the earth, yes, as there are air molecules which slowly slow you down because of friction, so theoretically, if you keep on travelling from side to side, you will end up trapped on the centre of the earth.

So, i hope i've helped those of you who didn't know it and were interested to find out the answer.

berkeman

Welcome to the PF.

This is actually a frequently asked question here on the PF. You have it mostly right, but you do not accelerate at 9.8m/s^2 all the way to the center of the Earth. Do you know why not?

TGlad

Also, would the rotation of the earth affect your trajectory?
Let's say that the hole is on the equator and that it does take 21 minutes to travel earth's radius, whatever velocity vector you had at top speed (at the earth core) you might be displaced by 586km when you exit.
So this might mean that the hole would need to be 586km wide (long) at least.

Chronos

The coriolis effect would be a factor unless your shaft passed from pole to pole. Another issue would be air resistance, which limits terminal velocity to about 58 meters/sec for a typical adult human. Yet another factor is the density of earth increases with depth. The figure of 42 minutes for passing pole to pole is an idealized value that ignores air resistance and the density gradient.

bahamagreen

If you assume:

-Earth is not spinning
-Tunnel is frictionless
-No air resistance
-And probably something I'm missing

Then not only does it take "X" time to go from one end of the Earth to the other, but it also works out to take that same "X" time to go the full length of any straight tunnel though the Earth from any point on the Earth's surface to any other point on the surface... shallow tunnels like from DC to Boston, deeper ones like London to Paris, even deeper ones like Tokyo to Cairo... going between all surface points connected by straight tunnels through the Earth would take the same time...

TGlad

Is that true? If so it is quite an interesting fact, I like it!

Chronos

Yes, it does not matter what angle you drill the tunnel, it basically takes the same amount of time to 'fall' to the other side.

mfb

If it would be possible to dig those tunnels, you could create a global network with an 1-hour schedule ;).

For connections between points which are not opposite to each other, there are quicker, curved paths.

Chronos

Unfortunately, air resistance would both significantly limit your maximum free fall velocity and prevent you from 'falling' all the way to the other end of the tunnel.

Michael Redei

You could evacuate the hole, hold your breath and then jump into the entrance hole, so you'd "pop out" at the other end.

Vadar2012

In order to create the tunnel, you'd have to stop the flow of molten material at the Earth's core, thus interupting the Earth's magnetic field. So in order to conduct your experiment, you're killing an entire planet. Now that's an epic experiment.

BobG

You obviously didn't do the calculation yourself, since if you accelerate at 9.8 m/sec^2 for 6.378 million meters, then decelerate at 9.8 m/sec^2 for 6.378 meters, it won't take 42 minutes to get to the other side.

And while your 22,000 mph is at least in the ball park for constant acceleration, your km/h looks like it was just pulled out of thin air. (Hint: If your speed is in meters/second, doubling the value gets you at least in the ballpark for miles per hour. Not a very accurate estimate, but accurate enough to get a feel for the range you're talking about.)


Your rate of acceleration has to decrease all the way down and your rate deceleration increases all the way up to get 42 minutes (42 minutes, 20 seconds would be a more accurate answer).

Lsos

Since it looks like we're assuming air resistance, not only will there be "air molecules" slowing you down, but there will be ALOT of air molecules slowing you sown. Much more than on the surface. Depending on what assumptions we make, it could even be liquid.

Either way, even if we assumed normal air resistance I'm guessing you probably wouldn't make it more than a meter past the center.

surajt88

That seems accurate. Gravity train - wiki

sepa0202

Well of course, assuming it's an isolated system from the universe.
But if we had to carry this experiment out, we should take in account more things, such as air resistance.

mrspeedybob

True. At thr surface you've got a 50 mile or so column of air on top of you. By the time you got to the center youd be under a 4000+ mile column of air.

Chestermiller

The temperature would be above the critical temperature for both oxygen and nitrogen, so the air could not be liquified no matter how high the pressure got.