Suppose you could drill a hole through the Earth and then drop into it. How long would it take you to pop up on the other side of the Earth? The calculations are not simple, but the answer is 42 (minutes). Link -via Reddit
Ignoring the heat at the core, wouldn't you stop at the center due to gravity??
Ashley: No, because once you'd fallen that far, you would have gathered enough speed to shoot through the center. Gravity would then begin to slow you down, and discounting air resistance, you would pause for another moment at precisely the same height from which you dropped-- only on the other side. Again discounting air resistance, the oscillation could go on forever if you let it.
If I understand and remember my high school science correctly, we are pulled to the Earth because of the mass that it has. The mass of the Earth is what creates the gravitational field which keeps us from flying off into space. If that's the case, then when the person flying through the Earth-tunnel hits the dead-center of the Earth, would the gravitational forces from the mass all around him pretty much rip him apart? Just a thought...
@ M: Nope, just follow the link, it's explained pretty clearly:
"Your initial acceleration would be the surface acceleration of gravity but the acceleration would be progressively smaller as you approached the center. Your weight would be zero as you flew through the center of the Earth."
and
"If you drilled a hole through the center of the Earth, the acceleration of gravity would decrease with the radius on the way to the center of the Earth. If the Earth were of uniform density (which it is not!), the acceleration of gravity would decrease linearly to half the surface value of g at half the radius of the Earth and approach zero as you approached the center of the Earth."
@Retrokatze: I agree. Your comments make sense. But that all relates to acceleration. I'm not talking about the acceleration that the body is moving at. I'm talking about the gravitational forces acting on the body. Would the gravity pull apart the atoms of the body traveling through the tunnel?
Forget for a second that the body is traveling at all. Let's just say that at the very center of the Earth, there is a hollow center. So picture a spherical hollow room at the center of the Earth surrounded by miles and miles of rock around. If a person were to be placed in that room, would the gravitational forces generated by the mass all around him rip the atoms of that man's body apart? No acceleration involved...
You're sitting on the Earth, right? Imagine half the gravity acting on your body right now was above you, and the other half was below you -- do you think that would be enough to pull you apart? That's an oversimplification, but also the worst-case scenario. You wouldn't be pulled apart, you'd just be weightless -- and intact.
I'm not so sure that's the worst case scenario. After all, gravitation scales inversely with the square of distance, and in the center of the earth, you are closer on average to all parts of the globe than standing on its surface.
Still, I agree that it probably wouldn't be enough to overcome the cohesive forces holding your body together.
thanks for all the great explanations! yeah, I wasn't so sure it would be enough to rip the atomic bonds apart either, but just thinking about that scenario made me ponder whether or not u'd feel the forces pulling at u from all sides. thanks!
Thanks for the response. You're right. When I said, "worst-case scenario," I meant having all the gravitational force concentrated in two forces operating in direct opposition to one another -- meaning the scenario most likely to pull you apart. But you're right to say that the overall gravitational forces at the center of the Earth would be greater than that at the surface, absolutely.
... As this hole goes right through the earth, you could fall down it from both ends. As you approach the end of the tunnel, are you not flying instead of falling down ?
That's a fascinating twist, Ted: if your center is at the Earth's center, is gravity pulling you apart, or compressing you? Gravity pulls towards the center of the Earth, so if you're at the center, maybe it WOULD compress you -- but does the theoretical void (the tunnel) at the center of the Earth change that, since the actual mass that creates the gravity would be surrounding you? I think that mass would have to be inside of you in order to compress you...?
The answer is correct except for one thing ... friction from air. As you started to fall, you'd initially hit terminal velocity within a couple hundred feet - approximately 150mph. Even though the air's density might decrease a little as you approach the center, your speed wouldn't increase much due to the lower downward gravitational pull.
In the best case scenario, you might be hitting 400 or 500 mph at the core, which is about 17,000 mph slower than you need to pop out the other end. Even if you wore a special suit to keep out the ferocious heat, you'd be forced to live out the rest of your life virtually weightless at the center of the earth.
And, considering the Earth as a series of hollow shells one inside the other, it follows that you're not affected by the gravitational pull of the layers that are farther from the center than you are. At the center you feel the same as in free space, as others pointed out.
Anita, they state right off the bat, "For our hypothetical journey we will assume the Earth to be of uniform density and neglect air friction and the high temperature of this trip."
c-dub - I realize that, but the commenters seemed to be taking this a bit too seriously. Although I guess if we had the technology to drill thousands of miles through the earth (vs. our current record of a few miles), we'd also have the technology to vacuum seal the tube and ensure the traveler wouldn't burn up.
How would you get out of the vacuum-sealed tube, then?
As for compression, I was thinking more of the forces involved than the physical solid core of the earth, thus imagining that two things could occupy the same space at the same time - why not?
If there were a tube, presumably we would have the ability to negate any dangerous effects, but probably not the smarts to ensure that people don't jump in from opposite ends at the same time, or the ability to protect it from terrorists.
(That was actually a question on Car Talk once.)
"Your initial acceleration would be the surface acceleration of gravity but the acceleration would be progressively smaller as you approached the center. Your weight would be zero as you flew through the center of the Earth."
and
"If you drilled a hole through the center of the Earth, the acceleration of gravity would decrease with the radius on the way to the center of the Earth. If the Earth were of uniform density (which it is not!), the acceleration of gravity would decrease linearly to half the surface value of g at half the radius of the Earth and approach zero as you approached the center of the Earth."
'nuff said.
Forget for a second that the body is traveling at all. Let's just say that at the very center of the Earth, there is a hollow center. So picture a spherical hollow room at the center of the Earth surrounded by miles and miles of rock around. If a person were to be placed in that room, would the gravitational forces generated by the mass all around him rip the atoms of that man's body apart? No acceleration involved...
You're sitting on the Earth, right? Imagine half the gravity acting on your body right now was above you, and the other half was below you -- do you think that would be enough to pull you apart? That's an oversimplification, but also the worst-case scenario. You wouldn't be pulled apart, you'd just be weightless -- and intact.
I'm not so sure that's the worst case scenario. After all, gravitation scales inversely with the square of distance, and in the center of the earth, you are closer on average to all parts of the globe than standing on its surface.
Still, I agree that it probably wouldn't be enough to overcome the cohesive forces holding your body together.
post: und zwar hier.
What I wrote was: This is also explained on the webpage linked in the post.
Thanks for the response. You're right. When I said, "worst-case scenario," I meant having all the gravitational force concentrated in two forces operating in direct opposition to one another -- meaning the scenario most likely to pull you apart. But you're right to say that the overall gravitational forces at the center of the Earth would be greater than that at the surface, absolutely.
Also, I would want to make sure that nobody's jumping from the other side while I'm in there.
In the best case scenario, you might be hitting 400 or 500 mph at the core, which is about 17,000 mph slower than you need to pop out the other end. Even if you wore a special suit to keep out the ferocious heat, you'd be forced to live out the rest of your life virtually weightless at the center of the earth.
Quick! Build a fence to keep them from stealing our landscaping jobs!
As for compression, I was thinking more of the forces involved than the physical solid core of the earth, thus imagining that two things could occupy the same space at the same time - why not?
If there were a tube, presumably we would have the ability to negate any dangerous effects, but probably not the smarts to ensure that people don't jump in from opposite ends at the same time, or the ability to protect it from terrorists.