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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.
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.
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.
. . .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.
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
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
The earth's internal core is about 6000 C (source), and carbon in diamond form boils at 4027 C (source).
So, yes, diamond is still a known material.
Karma: Terrifying (mostly affected by atrocities you've committed)
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.