Digging Through the Earth: What Would Happen?

[Cal]

Hello,

Sorry if this is wrong section of forum. But i think its correct.

Ok, so this has always baffled me. If you could dig a hole through the Earth until you reached the other side, would you come out feet first? Of course, you have to take out of account the fact you would burn to death from the Earths core etc. Now of course this may sound stupid. But i have never understood it.

Could anyone of you people shed light on this theory?

Many Thanks in advance.

 

[Locrian]

I suspect you would come out shovel first.

 

[chroot]

Gravity will always pull you toward the center of the Earth. Once you passed the center of the Earth, gravity would be pulling you up, through the hole you've already dug above you, not down. I suspect you'd have to change your shovelling posture considerably.

- Warren

 

[nautica]

I don't see how he could continue shoveling up b/c there would be nothing to stand on after he had passed center, except the hole he had just dug. You would have to be not only shoveling but also climbing at the same time.

Nautica

 

[chroot]

nautica,

That was basically my point. You dig down till you get the center -- then you have to starting digging up.

- Warren

 

[Gokul43201]

You stick your legs outwards and pin yourself against the walls of the hole with friction. Or you carry a spring loaded jack to span the hole. You then straddle this, close your eyes and dig upwards.

You could dig downwards too, but you'll have to wrap your legs around the jack and be hanging upside down.

 

[chroot]

Either way, if I'm ever offered a job digging a hole through the earth, I'll probably turn it down.

- Warren

 

[Gokul43201]

Even if your life's ambition was to get to China ??!

 

[pebrew]

my favorite bit about digging through the Earth has always been that if you had a hole that went all the way through (pre-dug by a team of very fit dwarves, none of whose name is chroot) and you jumped in the hole you'd accelerate until you passed the middle and would then decelerate until you got to the other side china (er, australia), so you could take a step forward just as you got to the other side and be on standing on the ground. with no excess vertical velocity. and you would end up coming out feet first, unless you'd started with a some angular momentum and rotated on the trip down (and up). anyway, it's a nice consersvation of potential energy idea.

of course we are assuming things to be convenient to our desire to easily(?) travel through the Earth such as: a vacuum through our hole, thus no air friction, thus no terminal velocity. oh, and no very very very hot molten stuffs in the inbetweens. etc, etc.

 

[Andre]

Adding two cents to the conversation.

How long would it take to complete that fall up and down that hole, assuming no drag/friction and how would that compare to a theoretical orbit time of a satellite at Earth Surface level?

 

[Locrian]

Hey, I remember that problem from classical mech! If memory serves me, they are the same. I hope I'm remembering right, cause otherwise I'll have to get the pen and paper out :D

 

[nautica]

Either way, if I'm ever offered a job digging a hole through the earth, I'll probably turn it down.

- Warren

Yep, I believe someone was already offered the job back in the 50's or 60's. They were going to start at the bottom of the ocean. Then after millions of dollars were spent with only an 80 foot test hole to show for it they were fired. If my memory serves me correct the feasibilty study and the test hole cost more than the original estimates of the entire project.

An these people just wanted to get to the core. It would have really been exciting if they would have tried to dig out the other side.

Nautica

 

[Cal]

Thanks for all your replies people. I think i now understand it better. But, unless its actually attempted (which it proably never will) we would never know. All we have unfortunantly are theories.

 

[nautica]

No, it is a bit more than a theory, it is the law of gravity. Which says and has been proven that gravity starts at the center of the mass, not in the outer areas of the mass.

Nautica

 

[Integral]

Yep, I believe someone was already offered the job back in the 50's or 60's. They were going to start at the bottom of the ocean. Then after millions of dollars were spent with only an 80 foot test hole to show for it they were fired. If my memory serves me correct the feasibilty study and the test hole cost more than the original estimates of the entire project.

An these people just wanted to get to the core. It would have really been exciting if they would have tried to dig out the other side.

Nautica

Operation Mohole?

 

[arildno]

Adding two cents to the conversation.

How long would it take to complete that fall up and down that hole, assuming no drag/friction and how would that compare to a theoretical orbit time of a satellite at Earth Surface level?

I think the time down and back again would be approx. 42 minutes
(Or was that just one-way?)
Whatever the truth, 42 is definitely the answer to lots of stuff..

 

[nautica]

Operation Mohole?

Yep, if my memory serves me correct. It was headed by Hess. They were digging through the crust to study the history of the earth, continental drift, flow of heat from the interior, and formation of mineral resources. They planned to drill 18,000 feet, but the deepest hole ever dug before that time was only around 100 feet.

They asked the NSF for around $30,000, but were funded almost $80,000. After more money was spent it was turned over to Brown & Root, who had some connection with the government. The fiinal estimate I believe was around $67 Million and I don't exactly remember how much was actually paid to Brown & Root, but it was alot.

Finally, congress put a stop to it in the late 60's.

Big Science at its best.

Nautica

 

[Gokul43201]

Hey, I remember that problem from classical mech! If memory serves me, they are the same. I hope I'm remembering right, cause otherwise I'll have to get the pen and paper out :D

I second that. It looks like the time period of oscillations is independent of the path taken by the tunnel joining two fixed points on the surface...unless I'm making a mistake somewhere.

That's neat !

 

[Integral]

Adding two cents to the conversation.

How long would it take to complete that fall up and down that hole, assuming no drag/friction and how would that compare to a theoretical orbit time of a satellite at Earth Surface level?

This would be especially nice to know when you are digging your way back up... So you could duck when a shovel full of dirt comes back to you!

 

[PIT2]

I have a question about this. Suppose you did dig a hole and jumped into it, you would float in the center right? But... would you be crushed to death by the gravity?

 

[pebrew]

Nope. In fact, there'd be essentially no gravity. Not from the Earth anyway. Since there is no gravitational effects at the center of mass for a uniformly mass-distributed spherically symmetric object. All the gravity forces of the various pieces of Earth cancel out because they are uniformly distributed around you. The Earth isn't actually perfectly uniformly distributed and spherical, but it probably is close enough that you wouldn't notice any gravity.

hmm, which makes me wonder if the moon would affect your floating much.

 

[chroot]

pebrew:

That is correct, but you're reaching the wrong conclusion. It is true that the net gravitational force at the center of the Earth is zero. You would be weightless there. However, there would also be enormous pressure there, resulting from all the rocks "on top of you" in every direction. You would not feel any gravitational force, but you would most certainly be crushed by the pressure.

- Warren

 

[Andre]

One more thing, you would indeed end up at the centre, but it would take a while since you are now subjected to the response characteristix of a second order open loop system, you know, the mass below a string or an electrical circuit containing a capacitor and a coil. You would fall past the centre of the Earth (due to mass inertia) and then the increasing gravity would slow you down and pull you back eventially (spring effect)and so on. The air friction would dampen the motion until you end up at the centre after many oscillations.

http://math.stcc.edu/DiffEq/DiffEQ51.html is the idea.

And http://sysdyn.clexchange.org/gsp98/papers/D-4731.pdf is a very romantic version

 

[pebrew]

pebrew:

That is correct, but you're reaching the wrong conclusion. It is true that the net gravitational force at the center of the Earth is zero. You would be weightless there. However, there would also be enormous pressure there, resulting from all the rocks "on top of you" in every direction. You would not feel any gravitational force, but you would most certainly be crushed by the pressure.

- Warren

yes, that's probably the realistic outcome.


i was thinking of a more unrealistic case where there is an open tunnel through the Earth helf open by some sort of (very very very) strong supports so that the rock would not collapse. i guess i would also assume a vaccuum. since, even if you did have a tunnel like that the mere air pressure would be, to say the least, very intense at the center of the earth.

suffice it to say. there'd be a lot of practical problems tunnelling down theres.

 

[Bruce Wayne]

Adding two cents to the conversation.

How long would it take to complete that fall up and down that hole, assuming no drag/friction and how would that compare to a theoretical orbit time of a satellite at Earth Surface level?

I don't know exactly how long it will take to dig that hole, but assuming you already completed digging, it would take you about 18 minutes to fall out the other end. Also, your hole doesn't have to be directly down, it could be at an angle. Example, if you live in Los Angeles you can dig slanted hole to London and it will take you nearly 18 minutes to fall/slide out the other end. Of course, you will need to hold on to something or you will fall directly back to L.A. It will also be the same amount of time if lived in L.A. and dug to Sydney, Nairobi, or Beijing.

 

[ShakyJake]

I don't know exactly how long it will take to dig that hole, but assuming you already completed digging, it would take you about 18 minutes to fall out the other end. Also, your hole doesn't have to be directly down, it could be at an angle. Example, if you live in Los Angeles you can dig slanted hole to London and it will take you nearly 18 minutes to fall/slide out the other end. Of course, you will need to hold on to something or you will fall directly back to L.A. It will also be the same amount of time if lived in L.A. and dug to Sydney, Nairobi, or Beijing.

I saw this on an episode of The Universe. If you dug a tunnel between ANY two points on Earth it will always take the same amount of time to "fall" to the other side. Although I thought the time was on the order of ~40 minutes not 18.

 

[Bruce Wayne]

Hmm, not sure really. You could be right. I think that's where i got the info at first. I'll investigate and give out the real time ASAP.

 

[DaveC426913]

I saw this on an episode of The Universe. If you dug a tunnel between ANY two points on Earth it will always take the same amount of time to "fall" to the other side. Although I thought the time was on the order of ~40 minutes not 18.

The time it takes to make one complete trip through the Earth and back is exactly the same time it would take to do it in a hypothetical orbit outside the Earth at 0 altitude: namely about 90 minutes. This is not a coincidence.

 

[Bruce Wayne]

The time it takes to make one complete trip through the Earth and back is exactly the same time it would take to do it in a hypothetical orbit outside the Earth at 0 altitude: namely about 90 minutes. This is not a coincidence.

I know I heard 18 minutes from somewhere, can't recall. strongly apologize to all Physics Forum users for my mistake. Thanks for catching my mistake.

 

[DaveC426913]

strongly apologize to all Physics Forum users for my mistake.

We forgive you. This time. Next time it'll be the rack for you.