Posted on 04/19/2014 8:40:10 AM PDT by doug from upland
Q: If you could drill a tunnel through the whole planet and then jumped down this tunnel, how would you fall?
Posted on August 3, 2012 by The Physicist
Physicist: This is a beautiful question, in a small part because it’s an interesting thought experiment with some clever math, but mostly because of all the reasons it couldn’t be done and wouldn’t work. Right off the bat; clearly a hole can’t be drilled through the Earth. By the time you’ve gotten no more than 30 miles down (less than 0.4% of the way through) you’ll find your tunnel filling will magma, which tends to gunk up drill bits (also melt everything).
Jumping into a hole drilled through the Earth. What’s the worst that could happen?
But! Assuming that wasn’t an issue, and you’ve got a tube through the Earth (made of unobtainium or something), you still have to contend with the air in the tube. In addition to air-resistance, which on its own would drag you to a stop near the core, just having air in the tube would be really really fatal. The lower you are, the more air is above you, and the higher the pressure. The highest air pressure we see on the surface of the Earth is a little under 16 psi. But keep in mind that we only have about 100 km of real atmosphere above us, and most of that is pretty thin. If the air in the tube were to increase in pressure and temperature the way the atmosphere does, then you’d only have to drop around 50 km before the pressure in the tube was as high as the bottom of the ocean.
Even worse, a big pile of air (like the atmosphere) is hotter at the bottom than at the top (hence all the snow on top of mountains). Temperature varies by about 10°C per km or 30 °F per mile. So, by the time you’ve fallen about 20 miles you’re really on fire a lot. After a few hundred miles (still a long way from the core) you can expect the air to be a ludicrously hot sorta-gas-sorta-fluid, eventually becoming a solid plug.
But! Assuming that there’s no air in the tube, you’re still in trouble. If the Earth is rotating, then in short order you’d be ground against the walls of the tunnel, and would either be pulverized or would slow down and slide to rest near the center of the Earth. This is an effect of “coriolis forces” which show up whenever you try to describe things moving around on spinning things (like planets). To describe it accurately requires the use of angular momentum, but you can picture it pretty well in terms of “higher things move faster”. Because the Earth is turning, how fast you’re moving is proportional to your altitude. Normally this isn’t noticeable. For example, the top of a ten story building is moving about 0.001 mph faster than the ground (ever notice that?), so an object nudged off of the roof can expect to land about 1 millimeter off-target. But over large changes in altitude (and falling through the Earth counts) the effect is very noticeable: about halfway to the center of the Earth you’ll find that you’re moving sideways about 1,500 mph faster than the walls of your tube, which is unhealthy.
The farther from the center you are, the faster you’re moving.
But! Assuming that you’ve got some kind of a super-tube, that the inside of that tube is a vacuum, and that the Earth isn’t turning (and that there’s nothing else to worry about, like building up static electricity or some other unforeseen problem), then you would be free to fall all the way to the far side of the Earth. Once you got there, you would fall right through the Earth again, oscillating back and forth sinusoidally exactly like a bouncing spring or a clock pendulum. It would take you about 42 minutes to make the trip from one side of the Earth to the other.
The clever math behind calculating how an object would fall through the Earth: As you fall all of the layers farther from the center than you cancel out, so you always seem to be falling as though you were on the the surface of a shrinking planet.
What follows is interesting mostly to physics/engineering majors and to almost no one else.
It turns out that spherically symmetric things, which includes things like the Earth, have a cute property: the gravity at any point only depends on the amount of matter below you, and not at all on the amount of matter above you. There are a couple of ways to show this, but since it was done before (with pictures!), take it as read. So, as you fall in all of the layers above you can be ignored (as far as gravity is concerned), and it “feels” as though you’re always falling right next to the surface of a progressively smaller and smaller planet. This, by the way, is just another reason why the exact center of the Earth is in free-fall.
The force of gravity is F = -\frac{GMm}{r^2}, where M is the big mass, and m is the smaller, falling mass. But, since you only have to consider the mass below you, then if the Earth has a fixed density (it doesn’t, but if it did) then you could say M = \rho \frac{4}{3}\pi r^3, where ρ is the density. So, as you’re falling F = -\left(\frac{Gm}{r^2}\right)\left(\rho \frac{4}{3}\pi r^3\right) = -\left(\frac{4}{3}G\rho \pi\right) mr.
Holy crap! This is the (in)famous spring equation, F = – kx! Physicists get very excited when they see this because it’s one of, like, 3 questions that can be exactly answered (seriously). In this case that answer is r(t) = R\cos{\left(t\sqrt{\frac{4}{3}G\rho \pi} \right)}, where R is the radius of the Earth, and t is how long you’ve been falling. Cosine, it’s worth pointing out, is sinusoidal.
Interesting fun-fact: the time it takes to oscillate back-and-forth through a planet is dependent only on the density of that planet and not on the size!
Way too funny. It was while trying to find the source of that clip that I stumbled upon this science question.
No but an EENT man would help.
The tube, in the hole I drilled to tour the NAZI UFO collection, doesn’t have frictionless sides. I got around the Coriolis-effect problem by drilling along the rotational axis, from the North pole to the south pole. There’s still a bit of pull from the moon & the sun (like my own tidal forces); but, I get around that riding a skate board down the sides of the tube.
https://www.youtube.com/watch?v=cGbEE-1hA2s - look at the 40 second mark.....several million degrees...BWAHAHAHAHA
Actual is now estimated at about 10,800 F
Very exciting thread!
When I was in 5th grade I used to debate this with the 7th grade crossing guard. I think his name was Craig. We concluded:
A) It was not possible to bore a hole through the center of the earth, but!
B) For arguments sake, if you could, you would not be able to jump in and pop out the other side. Air resistance and friction would slow you down and you would come to rest at the gravitational center of the earth.
What we did not consider getting squished or heat vaporized by air pressure, but then we were still only in Grammar school.
Same leftists. Different topics.
I've heard this answer before, also referencing the Chinaman's point of view which was seeing somebody falling UP out of a hole.
The BLM would be there waiting to say it was theirs.
Yes, that's what our physics professor said in college. You'd (theoretically) oscillate from one end to the other.
This is the same as the “penny dropped from a skyscraper lands a millimeter to the side” in another comment, or not?
BWAHAHAHAHAHAHAHA!
Beck interviews Brian Whitman as Algore.
https://www.youtube.com/watch?v=LkAh43KhONw
ANOTHER INTERVIEW: https://www.youtube.com/watch?v=HfB5sjMGTDw
Hell, I thik we are living in Upsidasium now!
(btw isn’t that Boris Putin in middle??)
ROTFLMAO!
Doug,
Thanks for the fascinating dissertation on a question we’ve all asked at one time or another.
Wonder if the results would be the same if we dumped obozo into that tunnel?
My guess is that the earth would expel him via a spasm of projectile vomiting!
I might regret asking, but...
Isn’t it likely that at some point the center of gravity relative to your location would pull you into the wall of the tube?
I once saw a heavy tool let loose into the bore of a powerful MRI magnet. Bearing in mind that the center of the magnetic field is in the very center of the bore, the tool shot through to the other end then came back, oscillating several times before coming to rest in the center. It was as frightening as it was cool to watch. BTW, the idiot who brought a magnetic tool into the room was kicked off the job.
The globe really is warm!
But the falling cables cut the car (and him) in half.
Scary. Here's a nightmare for ya:
http://www.dailymotion.com/video/x11gx3_damien-omen-ii_news
What is the Farthest any one has ever gone underground?
Any human to be specific :)
plz answer
Best Answer
Dan S answered 7 years ago
The Russians have gone over 4.8 miles down.
The project was first proposed in 1962 and was assigned to the Interdepartmental Scientific Council for the Study of the Earth’s Interior and Superdeep Drill. The Russians stopped drilling when it got too hot 180 °C (356 °F), but they expect to continue to a final depth of 1,500 meters with an expected temperature at 300 °C (572 °F).
The deepest any human being has gone down is 3,774 meters (1.48 miles) in South Africa.
According to Wikipedia: http://en.wikipedia.org/wiki/Mining#Reco...
“The deepest mine in the world: Savuka Mine in the North West Province, South Africa at 3,774 meters.
The deepest borehole in the world: Kola Superdeep Borehole at 12,262 meters (4.8157 miles). This, however, is not a matter of mining but rather related to scientific drilling.”
According to Wikipedia: http://en.wikipedia.org/wiki/Kola_Superd...
“The Kola Superdeep Borehole (KSDB) was the result of a scientific drilling project of the former USSR. The project attempted to drill as deep as possible into the Earth’s crust. Drilling began on May 24, 1970 on the Kola Peninsula, using an “Uralmash-4E” and later an “Uralmash-15000” drilling device. A number of boreholes were drilled by branching from a central hole. The deepest, SG-3, was completed in 1989, creating a hole 12,262 metres (7.6 mi) deep, the deepest hole ever made by humans...
It was decided to drill again from 7,000 metres (22,970 ft)[3]. The hole reached 12,262 metres (40,230 ft) deep in 1989. In that year the hole depth was expected to reach 13,500 metres (44,290 ft) by the end of 1990 and 15,000 metres (49,210 ft) by 1993. However, due to higher than expected temperatures at this depth and location, 180 °C (356 °F) instead of expected 100 °C (212 °F), drilling deeper was deemed infeasible and the drilling was stopped in 1992. With the expected further increase in temperature with increasing depth, drilling to 15,000 metres (49,210 ft) would have meant working at a projected 300 °C (572 °F), at which the drill bit would no longer work.”
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