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The Science of a Bottomless Pit
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.
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
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
Does anyone else remember an issue of OMNI magazine from the early 1980s that discussed this? I think it may have been around 1982.
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.
- ------ Go 'til ya know.
This very topic is discussed in "Entertaining Physics" printed first in 1912. And I'm sure it has been discussed even earlier.
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.
If this were late December, this would be an article about the physics of Santa Claus having to travel to so many households per second that he'd be essentially a ball of flaming plasma. Which is to say, a singularly pointless thought experiment. But apparently it's not singular. We've gone past the pointlessness singularity. Paging Mr. Kurzweil!
Don't disappoint your bird dog. Go to the range.
Isn't that part of every physics student's first/second week as a freshman any more? Frictionless and full-of-vacuum tunnels and everything?
Free, as in your money being freed from the confines of your account.
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.
Bunkum. I saw the film "Journey to the Center of the Earth", and not only was there daylight down there but the climate was temperate, with lakes, and trees growing by them. The gravity was normal.
This is a scare story to keep trespassers away.
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.
The most complicated part of the problem: a passing through Hell, could be a difficult strategy problem, more than an engineering one.
In the Joint Entrance Examn for the IITs it used to be a common problem. I know from memory it would oscilate back and forth. 90 minutes period of so.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
. . .because it takes at least 1 hour at each end for ground transportation and you need to allow an hour to clear security, another hour at the other end for immigration and customs.
Should've started at the South pole... LDO
Which theory is that, exactly? The theory in material science that there's something to make the walls from that'd survive the pressure and heat of the Earth's core?
I actually live near a REAL one.
http://www.sciencebuzz.org/blo...
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.
-Styopa
Because after the first poor sap died at the mantle, it would take forever to convince he second poor sap to jump into the failed attempt at the hole.
"Win treats sysadmins better than users. Mac treats users better than sysadmins. Linux treats everyone like sysadmins."
.....Science is a Bottomless Pit.
The Science of the Bottomless Slut, AKA white ratchet girls with no booty. yes Miley, I'm lookin' at you...
Is that what we've come to? Boiling down science to a 5th grade level?
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.
Fun fact, during the space race there was also a less well known "Drill race" between the Soviet Union and America to see who could dig down the farthest. The Soviets won this by a long shot and as always found a lot of things that changed what we know about the composition of the Earth's crust. Most notably the farther they went down they noticed that the mud that bubbled up contained hydrogen and lots of water. They also noticed that the rock type didn't change at those depths (the reason seismic waves travel around the center of the earth instead of through it). The rock actually began to behave more like plastic at those depths! Learn more here http://en.wikipedia.org/wiki/K...
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.)
http://www.geoffreylandis.com
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.
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 distances that start to be comparable to 10% of the Earth's radius, so it should be close to the miss distance.
It's a non-Keplerian orbit (even in the non-rotating frame), so you don't come back to the same place you started.
http://www.geoffreylandis.com
"This requires a lot of imagination, because the temperatures and pressures are so spectacularly large they would literally melt, boil or sublimate any known materials"
So diamond isn't a known material?
"but in theory, it should be possible to construct one,"
Pressure = Volume * Temperature
Good luck finding materials that can withstand the pressure and temperature more than 12 KM deep.
https://www.youtube.com/watch?v=zz6v6OfoQvs
This is where the fun begins!
But still, you get the point. :D
excitingthingstodo.blogspot.com
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 velocity
%x(3) = theta position
%x(4) = theta velocity
dx(1)= x(2); %Velocity
dx(2)= x(1)*x(4)^2-(.0037e-3*x(1)-3.35e-13*x(1)^2);
dx(3)= x(4);
dx(4)= (-2*x(2)*x(4))/x(1);
end
http://imgur.com/WHsoenC
This is relative to a fixed observer outside of earth.
If you subtract out the earth rotation you get this.
http://imgur.com/nMN2Hd7
I love Jesus, except for his foreign policy.
Looks like you, along with your moderators, failed those courses and need to go back and retake them.
http://www.straightdope.com/columns/read/154/what-if-you-fell-into-a-tube-through-the-earth
I repeat, nerd alert... :)
Tired of my customary (Score:1)
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.
http://www.geoffreylandis.com
Wouldn't a gooey center be the real problem?
What does the path of the hole look like, then?
Thanks. Now I just need to get motivated enough to do this in 3D for random points on a sphere.
I love Jesus, except for his foreign policy.
I would like to point out an interesting gravity phenomenon that would occur inside earth along the way to the center. Once you're about ½ to the center of earth, the force of gravity no longer acts as a point body pulling you in. You now have a slice of earth above you, pulling you up, while the remaining slice below you is pulling you down.
Whatsmore, the sum of the gravity forces will cease to be linear the very first few seconds of your fall. When the proximate mass above you is equal to the proximate mass below you, most of the effective pulling force has diminished. This occurs quite far from the center. You could say it is the surface mass of earth holding you down right now, not the entire earth and esp. not the mass on the opposite side of the planet. Earth's mass is melded together in this way, not because every particle of earth is pulled into the center.
Same is true with the Moon's satellite orbit around the earth, the most distant point of earth is not pulling the moon toward earth, it is the semisphere closet to the moon at any given time.
D:
hmm you would die. It would crush whatever vessel you use to travel through the tunnel. I highly doubt the tunnel will stay open. Do you have any idea of what's past the mantle ? Hot magma. The internal core of the earth has several layers, constructed as a dynamo. the inner layer actually spinning in the opposite direction. Don't believe me.. google it. it's amazing. If you survive the heat and pressure the electrical energy produced would finish you off.
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.
I'm building a scale model of the Earth. 1 mile = 1 mile.
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 clever ten-year-old could be extraordinarily high at an epsilon displacement from the centroid of a just-a-titch oblate, spherical mass, but then you'd have to postulate a tiny black hole at the turtle point, protected by a hard chocolate coating of quantum-gravity exclusion effect (or a really, really strong, short-distance-repulsive nuclear gasbag force).
Nobody else has mentioned that in the 2012 remake of Total Recall (with Colin Farrell), The Fall is a transportation system that connects one side of the world to the other side?
In the 1974 movie Genesis II, there is an underground network of trains. I do not recall if it was ever elaborated, but I always assumed that the routes were chords through the Earth.
World you jump head first or feet first.?
"And the fifth angel sounded, and I saw a star fall from heaven unto the earth: and to him was given the key of the bottomless pit."
Context - The Fifth Trumpet
1Then the fifth angel sounded, and I saw a star from heaven which had fallen to the earth; and the key of the bottomless pit was given to him. 2He opened the bottomless pit, and smoke went up out of the pit, like the smoke of a great furnace; and the sun and the air were darkened by the smoke of the pit.â¦
Notice: The "star" is a "he".
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.
You could try Portugal and New Zealand, where two pieces of bread were once placed simultaneously, making an Earth sandwich !
The earth wobbles because it has a moon.
Also, you couldn't just yo-yo forever. Induction drag would slow you down.
Best to degauss the Earth prior to long term gravitational bungee jumping.
We already have a bottomless pit... the IRS!
Every religious book wrote http://en.wikipedia.org/wiki/Flat_earth
Casteism