The Science of a Bottomless Pit 122
StartsWithABang writes It's the ultimate dream of many children with time on their hands and their first leisurely attempt at digging: to go clear through the Earth to the other side, creating a bottomless pit. Most of us don't get very far in practice, but in theory, it should be possible to construct one, and consider what would happen to a very clever test subject who took all the proper precautions, and jumped right in. Here's what you would have to do to travel clear through the Earth, come out the other side, and make the return trip to right back where you started.
(looks straight down) (Score:4, Funny)
hello perth australia from new york city
we're not your true antipodean doppleganger, that would be hamilton bermuda
but you're the closest thing to that for us
and if when they find Malaysia Airlines Flight 370 it turns out to be directly antipodal to the Statue of Liberty, i'm giving up on reason and becoming a conspiracy theorist
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Interesting... What happens if you tunnel fro New York into an ocean on the other side of the world? Does the water drop in and boil in the centre of the Earth?
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The USA would wage a never-ending War on Oceans.
Re:(looks straight down) (Score:5, Funny)
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This was what I was thinking about their example of a tunnel between the poles. Given that Arctic Ocean is more than 4km deep at the North Pole. Even with a vacuum tube you might fall around 7km short of the South Pole...
Re:(looks straight down) (Score:4, Insightful)
Since the gravitic center is essentially the Earth's center of mass, do we know if that point is dead-center? Given the differences in crust thickness, ocean placement, mountains, etc...?
Do I need to get more coffee?
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Gravity is non-linear, and assumed to be zero at the core.
* http://en.wikipedia.org/wiki/M... [wikipedia.org]
* http://en.wikipedia.org/wiki/F... [wikipedia.org]
* http://en.wikipedia.org/wiki/F... [wikipedia.org]
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More coffee all around.
Re:(looks straight down) (Score:4, Interesting)
"What happens if you tunnel fro New York into an ocean on the other side of the world?"
This is an interesting scenario. First, the amount of water it would take to fill the tunnel up to its center would be enough to slightly lower the water level, easing the flooding problem in places like Venice and Miami. The water near the center would boil, bubbling up through the water higher up in the tunnel to create a steady plume of steam at the surface. This would end up as increased cloud cover and precipitation over large parts of the world.
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The water near the center would boil, bubbling up through the water higher up in the tunnel to create a steady plume of steam at the surface. This would end up as increased cloud cover and precipitation over large parts of the world.
Really? I would think it would cool somewhere on the way up. Volcanic activity on the ocean floor that boils water doesn't make it to the surface as steam.
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The water higher up would cool the steam at first, but the Earth's internal heat would eventually create a large bubble of superheated steam. Inevitably, some of this would bubble through. Hopefully, not too much at a time.
Re:(looks straight down) (Score:5, Funny)
Re: (looks straight down) (Score:3, Funny)
You would have to place a sign or a ladder to the top of the tunnel to prevent the water from passing through
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I see what you did there...
Re:(looks straight down) (Score:5, Funny)
Worst. Haiku. Ever.
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seven hundred ten
seven hundred eleven
seven hundred twelve
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I guess that makes us one vertex of the Anti-Bermuda-Triangle. Its a wonder more planes haven't gone missing.
But we do still have some bits of your Skylab that crashed here. Coincidence?
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you guys need a better PR team
https://www.youtube.com/watch?... [youtube.com]
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OMNI (Score:3)
In that article, they estimated the roundtrip would take around 42 minutes, which I thought was a grand coincidence having just read The Hitchhiker's Guide to the Galaxy.
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Re:Fall time (Score:1)
Read the whole article. It says 24 hours to fall to the center due to wind resistance, and then you stop. If you remove the air, it estimates 45 minutes for a one-way transit, and 90 minutes for a round trip.
Re:OMNI (Score:5, Informative)
24 hours *if* you have air resistance. And then you're moving so slow that you barely get past the center.
Note that no vacuum is perfect so you will lose velocity. Their scenario should have started the person off at the south pole, not the north, for the extra altitude.
Note that the heat isn't really the materials problem that they make it out to be - it's an energy problem. You don't need a material that can withstand 4000, you just need cooling. And not linearly high cooling, but an exponential decline. The longer you cool the rock down to your target temperature, the deeper your effect on the rock temperature behind your tunnel walls, and thus the shallower the temperature gradient, and thus the lower the rate of heat loss. It's like trying to cool a hot house - the air conditioner really struggles in the beginning but it gradually becomes easier with time as the walls and everything inside the house cool down.
Now, the pressures, those are insane, and the normal approach to pressure maintenance on deep drilling - filling with a heavy mud - obviously wouldn't work here.
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Their scenario should have started the person off at the south pole, not the north, for the extra altitude.
The problem with a vaccum tube, though, is that it is closed at both ends. As much as it sucks coming to an early stop below the surface, slamming into the airlock is going to hurt, at a speed which would otherwise get you up for another 4km ;)
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How about a vacuum tube that was formed in a loop passing through Earth and then back around the outside? It would need to be around 8000 miles in diameter (as a circle), since Wolfram Alpha says Earth's radius is 3957 miles. The tunnel would have a circumference somewhat over 25,000 miles.
The engineering is left as an exercise to the reader.
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The problem with a vaccum tube, though, is that it is closed at both ends. As much as it sucks coming to an early stop below the surface, slamming into the airlock is going to hurt, at a speed which would otherwise get you up for another 4km ;)
The fix is to make the "short" end of the tube taller, so that it sticks up above the Earth's surface as much as necessary. Oh yeah, and put a handrail next to the airlock.
Re:OMNI (Score:5, Funny)
Their scenario should have started the person off at the south pole, not the north, for the extra altitude.
Um, hello?
Everyone knows that north is on top, and you can't fall upwards.
The level of scientific illiteracy here is disgraceful.
Re:OMNI (Score:5, Interesting)
I always told my kids it takes longer to drive north because it's all uphill.
Interesting to watch their reactions over the years go from unquestioning acceptance, to cognitive dissonance. to enlightened disagreement, to "Daaaaaaad!!!", to "When are we stopping to dinner?'.
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Well considering that the Mississippi flows from North to South, and water flows downhill, I think you were more right than you realize.
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Reminds me of this Muse video [youtube.com]
Unfortunately music video producers are useless at science, he falls through and keeps going! Not only that, the video is much less than 42 minutes long.
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In that article, they estimated the roundtrip would take around 42 minutes
But what is really cool is that the time is the same for any chord, not just a diameter. So you could build a straight-line tunnel from New York to Los Angeles, completely evacuate the air, and then run frictionless trains through it, and they would transit the tunnel in 42 minutes, using NO fuel.
The walls of the tunnel could be made of Scrith, the same material used to construct Ringworld [wikipedia.org].
Kinda notnews (Score:5, Interesting)
Mathematically it's an example of a degenerate orbit with one zero semi-axis, and the orbital period can be simply calculated from Kepler's laws.
What's more interesting, it even holds true if you do not move through the center of the Earth! For example, a train from any place on Earth to any other place on Earth will move all by itself and always arrive at destination in about 45 minutes (neglecting the oblateness of the Earth and need to compensate for Coriolis forces and friction) if you put it inside a completely straight tunnel.
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Mathematically it's an example of a degenerate orbit with one zero semi-axis, and the orbital period can be simply calculated from Kepler's laws.
Indeed. Never thought of it that way, interesting.
Non Keplerian [Re:Kinda notnews] (Score:5, Informative)
Mathematically it's an example of a degenerate orbit with one zero semi-axis, and the orbital period can be simply calculated from Kepler's laws.
No, it can't; it's not a Keplerian problem. You could calculate the period using Kepler's laws if the Earth were a point mass. But it's not. You could calculate the period using the Brachistochrone calculation if the Earth were a uniform sphere. But it's not. The Earth is layered, with the density changing as you go closer to the center. Only way to solve the problem correctly is numerical integration.
(I'd actually be interested in seeing the calculation done in the article.)
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The Earth is layered, with the density changing as you go closer to the center
But in this case we're not only falling towards the center, but moving away from it as well. If we assume earth's layering to be similar in both halves, why aren't the effects you mentioned during the fall compensated for during the rise?
No, takes 4 hours 45 min . . . (Score:4, Funny)
Re:Kinda notnews (Score:4, Informative)
No its not. Because the problem is not central force motion between two point objects. The attracting mass effectively decreases as the object descends. A simple application of Gauss's Law. The motion of an object falling through a bottomless pit is harmonic [yahoo.com], not Keplerian.
Re:Kinda notnews (Score:4, Informative)
Mathematically it's an example of a degenerate orbit with one zero semi-axis, and the orbital period can be simply calculated from Kepler's laws. What's more interesting, it even holds true if you do not move through the center of the Earth! For example, a train from any place on Earth to any other place on Earth will move all by itself and always arrive at destination in about 45 minutes (neglecting the oblateness of the Earth and need to compensate for Coriolis forces and friction) if you put it inside a completely straight tunnel.
Nope, this is not "an example of a degenerate orbit with one zero semi-axis" and Kepler's first and third laws do not apply. Kepler's laws do not apply when you are falling through a sphere (or ellipsoid) that has its mass spread throughout its volume.
The orbit is not elliptical. Because the acceleration is not at all proportional to inverse of the squared distance. But if you plot the orbit, it does look a lot like an ellipse with a small semi-axis.
Kepler's second law applies due to conservation of angular momentum.
The calculation of the orbit is made more difficult because the density of the Earth varies from about 3 g/cm^3 to 13 g/cm^3. (We should be able to compute it pretty easily with Runge-Kutta.) To computer the orbit, we could reference the acceleration graph on the "Structure of the Earth" Wikipedia page.
http://en.wikipedia.org/wiki/S... [wikipedia.org]
Cyberax's second comment about the train (on a frictionless track) is really cool. I wonder how much the Coriolis force would affect the travel time.
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I wonder how much the Coriolis force would affect the travel time.
I guess the Coriolis affect would not affect the train's travel time because F_Cor = - 2 Omega x Vel and thus it is perpendicular to the direction of travel.
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OK I created the following Matlab code: The G term was a polynomial best fit to the gravity as a function of depth. The initial angular velocity is at the equator.
[t,y]=ode45(@orbit_ode,[0 200],[6500 0 0 2*pi/(24*3600)]);
polar(y(:,3),y(:,1))
function dx=orbit_ode(t,x);
dx=zeros(4,1);
%x(1) = r position
%x(2) = r velocity
%x(3) = theta position
%x(4) = theta velocity
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You miss the center by how much? [Re:Kinda notnews (Score:3)
OK I created the following Matlab code:
Cool!
The plot isn't very impressive. It looks like a line straight through the center. The min radius is 114m so basically over 6500m drop the center moves about 114 m.
That doesn't seem right. You are doing the calculation in the rotating coordinate system of the Earth?
Equatorial rotational velocity of the Earth is 465 m/s. The center of the Earth is stationary in the rotating coordinate system, so over a 22 minute drop, the lateral displacement should be 614 kilometers. That's not the distance by which you miss the center, since as you deviate from the initial radial line the gravity vector changes direction, but the effect of that will be small until you get to
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Great check! I found my error. My G calculation was pulled from a chart where the distance was measured in km (not meters). Here is the new code. This shows it takes about 19 minutes to reach the center and you miss by 310 km.
[t,y]=ode23(@orbit_ode,[0 90*60],[6500e3 0 0 2*pi/(24*3600)]);
polar(y(:,3),y(:,1))
min(y(:,1))
function dx=orbit_ode(t,x);
dx=zeros(4,1);%This is a pre-initialization.
%x(1) = r position
%x(2) = r velocit
Great graphs! Re:You miss the center by how much?] (Score:2)
Wow- that's cool. Thanks for the graphs!
I never would have guessed that for the rotating coordinate system the trajectory would be so very close to a straight line, although once you graph it, it makes sense.
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Thanks. Now I just need to get motivated enough to do this in 3D for random points on a sphere.
Santa Claus (Score:1)
Re: Santa Claus (Score:2)
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From the various studies, I have seen (including my personal observation) Santa had to make only 123 stops last year. As he has 24 hours to make the trip, that averages out to around 1 house every 30 minutes. He didn't even break a sweat.
Of course, it would be a very different case if the bad kids hadn't start igniting the coal, causing Santa to discontinue that tradition.
Math correction (Score:2)
But still, you get the point. :D
Physics 101 (Score:3)
Re:Physics 101 (Score:4, Funny)
No. In today's university, the entire first undergraduate semester is spent on sensitivity awareness, wymyn's studies, black history, and overcoming white privilege.
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Where's the spherical cow ?
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Journey to the Center of the Earth (Score:3)
This is a scare story to keep trespassers away.
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Just like the documentary I saw about how Abe Lincoln was a vampire slayer. It's a shame the history books didn't mention that.
"See? This is what we're talking about!" -- Oklahoma legislature
Does the pit have to be straight down? (Score:5, Interesting)
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The article suggests that the earth's rotation would cause the dropped to hit the wall on the way down. So why can't the tunnel curve to account for this? Presumably it would curve the other way as it exits. It also suggests that going from North to South pole wouldn't work because of their relative altitudes, but is there an antipodal point where the altitudes are close enough feasibly go from one side to another - e.g. build a tunnel / raised platform to bring each side to the same altitude. I realise this is all completely hypothetical, bad movie remakes notwithstanding.
You are going to have to excavate quite a bit of material. It seems like that would be a handy thing to do, build yourself a shield volcano around the entry point to get above sea level. And then on one side, build a hill or cliff to make entry high enough on the near side to get to entry on the other side.
See, this is what happens when you let theoretical physicists dream about stuff. Sometimes you need less Dc Cooper and more M. Eng Wolowitz.
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Easier to install guide rails. Plus you can use them for motors to compensate for any friction.
Given the speed, you could probably carry some magnets and make the shaft lining conductive. Inductive repulsion would push you away every time you got near. You'd lose velocity though, so you'd need a propulsion system to compensate.
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How high is the area around Madrid, Spain
I did Physics 101 at Massey University, in NZ
Traffic management would be crucial, what happens if a capsule from NZ and one from spain are in the tunnel at the same time
Anyway if we had the technology to drill even a tenth of the esy to the centre of the earth, our energy nrrds would be solved.
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our energy nrrds would be solved.
I know it's just a simple neighboring key typo, but I'm still laughing about a problem with "energy nerds" two minutes later.
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You could but it isn't a simple shape since the earths gravity changes as a function of radius in a pretty non-linear way.
http://en.wikipedia.org/wiki/S... [wikipedia.org]
Beware of the chert (Score:2)
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It is a common problem in JEE (Score:2)
"in theory, it should be possible to construct..." (Score:2)
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He proposed graphite with an active cooling system. That might be able to withstand the heat, but the pressure is going to be a lot harder.
The SD poster's theory (Score:1)
Slashdot summary:
in theory, it should be possible to construct one
Actual article:
Yet, despite the pressure and temperature gradients all the way down, despite having a liquid, molten outer core and a radioactive nickel-iron-cobalt inner core at over 4000 F, lets assume youve gone and physically created created something that will stabilize your cylindrical shaft going right through the Earths center.
no big deal (Score:5, Interesting)
I actually live near a REAL one.
http://www.sciencebuzz.org/blo... [sciencebuzz.org]
No, seriously, it's a hole in the ground, into which half of a decent-sized river dumps.
They have put everything from dye, to pingpong balls, to (amusingly) a car - and none of it has ever come up anywhere.
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I think we should throw a waterproof GPS down that hole and track where the exit is...
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It would take forever. (Score:2)
And when you REALLY get down to it..... (Score:2)
Written for a 5th grader? (Score:1)
Is that what we've come to? Boiling down science to a 5th grade level?
They did this right in a Warner cartoon (Score:2)
I can't find the video, but there was an episode of Tiny Toons or Looney Toons where one of the characters fell into a hole all the way through the moon or an asteroid, and he just kept oscillating back and forth.
Drilling race between soviets and Americans (Score:5, Interesting)
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"We must not allow a mine shaft gap!"
Obviously you had to bring this up from the Stanley Kubrick movie, but perhaps that line from the movie Kubrick was on to something. He did a lot of research prior to making Dr. Strangelove (probably had others do the same). There was a proposed "dooms day machine" like described in the movie but Khrushchev didn't approve it (that weapon system was too insane). I talked to a B52 navigator who flew missions in 1960s, he said Kubrick must have got info from SAC as procedures were much like the early A models
90 minutes (Score:2)
Is the 90 minutes required to make a round trip related to the minimum orbit time of about 90 minutes? They're both free fall journeys.
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One orbit has an eccentricity close to 0 (a large circle) whose radius exceeds the size of the planet.
The other orbit has an eccentricity that approaches 1 (a large, elongated ellipse, verging on a straight line), whose width (short diameter) is less than the diameter of the bottomless pit and whose length (long diameter) exceeds that of the
orly? (Score:2)
So diamond isn't a known material?
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The article suggested graphite with active cooling. Graphite is good up to around 4000k. You only need keep it 2000k below ambient - something that could be done via an active cooling system. You'd need need a pumping station the size of a city. It'd be a real mega-project, eclipsing anything in human history by orders of magnitude, but it's doable in theory. Just ridiculously impractical.
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Straight Dope covered this in 1979... (Score:1)
http://www.straightdope.com/columns/read/154/what-if-you-fell-into-a-tube-through-the-earth
Nerd Alert... (Score:2)
paradoxically (Score:2)
I'm pretty sure that 80% of the time that the word "paradoxically" shows up, what it really means is "don't worry your pretty freckles thinking too hard".
Maybe we need to invent the companion word "patradoxically" to mean "this is actually completely obvious, but since you have freckles, we'll pretend that it isn't".
I suppose some law of gravity as conceived by a cl
It's already happened! (Score:1)
Flat earth (Score:1)