If there were a tunnel directly through the center of the earth what would happen when someone jumped in?

Question

Would they shoot out the other side? Bounce back and forth until they eventually sit suspended in the exact center? Or maybe you would gain speed until you hit terminal velocity, then as you get closer to the center your speed would slow down until you come to a slow and gentle stop at the center? Discuss.

And I know you can't actually build that tunnel so don't bother to mention the impossibility. It's hypothetical. ;-)

Answer 1

Okay frist, all you dingbats who say "as you approach the center you would gradually slow down" I ask you this question: What experience in your life leads you to believe that as you crash toward the earth you slow down? Try jumping off a building and see if you gradually slow down. No. In fact, as you approach the center of the earth, the force of gravity acting on you would INCREASE and therefore you'd speed up. The radius (r) of the earth is about 6,378km. This means after you fell 3,200km, the force of gravity would be FOUR TIMES as strong as on the surface. Of course, in the center, you would appear "weightless" since all your parts would be pulled toward the center (silly as you'd most likely be squashed.

So, let's for the sake of argument say that you're squash-proof and there is no air in this heat-proof tunnel and therefore no air resistance. So we're tucked away in our safe pod poised on the lip of our pure-vaccum tunnel about to plummet toward the center of the earth. We tip forward and ZOOM!

Immediately we begin to plummet towards the center of the earth at 9.8 m/s^2 (G). Of course, you're in freefall so you feel weightless the entire time, even though your accelerating towards the earth at 1 G. This is similar to being in an elevator with the cables cut. If you had the presence of mind to have a scale with you and you weren't panicked about being flattened when you hit the basement, you could step on the scale and it would read 0.

After about 19 seconds of this pleasant weightlesses, you're travelling at about 11,000 m/s (or about 25,000 mph). This is when you ZOOM through the center of the earth. You are not gently slowling down here, you are going nearly 36 times the speed of sound (of course since it's a vaccum there is no sound).

Instantly the force of gravity switches to the reverse of your direction of travel and starts to PULL YOU BACK at 9.8 m/s^2 so that you are slowing down at exactly the same rate you accelerated at over the eact same distance (the radius of the earth). This time, however, you are travelling in the opposite direction of the force of gravity so you can sit down, read a book and relax for the next 19 or so minutes until you reach the surface of the earth.

When you get to the surface again, for the briefest moment your pod will stop and you may want to step out quickly because it's going to start hurtling toward the center of the earth again. And, yes, it will continue to do this for eternity. With no outward force on the pod and the force of gravity contstanly pulling on it, it will oscillate back and forth for the rest of time (or until the earth collapses). One round trip will take about 80 minutes and a one way will be about 40. You'll be weightless on your way "in" to the earth and a comfortable 1 G (your weight) on your way "out" to the surface.

Hope this clears it up for you.

* Note: What I didn't account for here, because I didn't have the time or the patience, was that G actually increases as you approach the center of the earth (it would be 4G at 1/2 the distance) I simply assumed a constant G. This means that your round trip times will be a little less and your final speed as you cross the center will be a bit more.

Answer 2

Well, as has been pointed out, you would be a damped harmonic oscillator. The force you felt would decrease linearly towards the center and you would go back and forth past the center until you stopped. However one thing has been omitted by others, you would also get pushed against the eastern side of the tube on the way down and the western side on the way up by the Coriolis effect, further dampening your motion beyond just air resistance

Answer 3

First, you would fall towards the center. The rate of your acceleration would gradually decrease as you approached the core, eventually reaching exactly zero at the center of the earth.

Then, as you continued to travel through the tunnel at truly phenomenal speeds, you would gradually deaccelerate at an increasing rate. When finally you arrived at the opposite side of the earth, your velocity would reach exactly zero, like at the apex of a jump.

At this point, you would be well advised to grab onto something substantial, because if you don't, you will quickly begin another descent back through the earth.

Of course, all of this supposes that the tunnel is a perfect vacuum impermeable the titanic forces at work within the earth. But that's how it would work

Answer 4

Interesting question.
Given the option, I would say that one would probably burn in the center either way.
Otherwise, however, one's terminal velocity would be one's velocity at the exact moment (s)he passed through the very center, and would gradually slow down, then, as you mentioned, bounce back and forth until they eventually stop at the center. Instead of being suspended, though, my guess is that one'd land on the side of the tunnel that has the greatest mass.

(NOTE: Oh, and according to Newtonian physics, GRAVITATIONAL PULL ACTING ON A GIVEN OBJECT TOWARDS A BODY OF MASS IS STRONGER THE CLOSER THAT THE GIVEN OBJECT IS TO THE BODY OF MASS. Ahem, F=g=(G[m1][m2])/r^2 -- look up the formula for gravitational pull.

Answer 5

If there is such tunnel and one body can withstand the temperature and other conditions, then it will oscillate about the center of the earth. The oscillation is damped if you consider the air friction. Since you are falling towards the center due to the gravitational force your potential energy will be converted to kinetic energy and at the center whole energy will be in the form of kinetic energy. So you'll move on to the other side and your potential energy will increase. This process repeats till all the energy is dissipated due to air damping.

Answer 6

Terminal velocity is a resistance phenomenon. Let's set it aside for the moment. If the tube is frictionless and air/gasless, the forces pulling you down are vector forces resolvable into down, sideways and up. The sideways forces are balanced (you said through the center of the earth), and the other vectors depend on mass and the square of the distance from the center of mass.

The center of mass is the center of the earth, and while you're far from it, the much smaller amount of mass above you as you fall doesn't have much influence and you drop toward the center. However, you are accelerated by less and less mass, so your acceleration decreases, but not your velocity and, absent friction, you still build up momentum and kinetic energy, both of which have to be counteracted by gravity beginning to act on your body as you pass through the center of the earth. So, absent friction, you should just make it out the other side at v=0. Grab on! so you don't have to head back.

Seems to me that friction or air resistance (terminal velocity) would only act in one direction, that of opposing your velocity vector, which would prevent you from attaining enough momentum to exit the hole, so you'd end up oscillating in the hole until coming to rest somewhere near the center. Somewhere near, btw, because at the center, the forces acting are all balanced, so it's possible that even a little tilt in your body, and you'll stick to one side of the hole, somewhat away from the center.

Answer 7

since it is a tunnel ,it is a open air space. An individual would fall in and might die from asphyexiation(lack of air,I am not spelling that right, apology) but if they survive they would eventually slowdown and would be trapped in the center.
Gravity waves at the center would actually slow them down into a spin at the center. They would remain at the center, spinning radically until a gravitational hickup occured
Oh they would have to have survived the heat?

Answer 8

This is actually a standard problem that all physics students are expected to solve, usually in a senior year mechanics course at university. The answer is that if there is no air resistance, you would oscillate back and force exactly like a simple harmonic oscillator (like a bob on the end of a spring).

Answer 9

Quick point - the force of gravity is decreasing as you fall down the hole. As you descend the mass 'under' you is less, so the gravitational field is less, decreasing to zero as you hit the center.

So, the main issue is air resistance (as the asker makes no mention of airless tubes, just a common or garden hole) Surely the density of air is increasing down the hole, so air resistance is increasing (however slightly) as acceleration by gravity is decreasing.

My gut feeling is that you'll still oscillate but it may be far slower than initially thought as you'll bleed off speed as the force acting on you decreases and the air resistance increases.

Answer 10

the effect of gravity decreases towards the middle (there is as much on one side as there is on the other, canceling out)

skydivers (freefall) hit terminal velocity pretty quick, 10 seconds or so, depending on posture thats anywhere from 120mph to 320mph (world record)

so, there you are falling at terminal velocity with 6,000 miles to go and the force due to gravity slowly decreasing.

you gradually slow down, wind resistance balancing net gravity untill you gradually approach the center.


edit

'hmm, just thought.. since a few mile thick of air (at the surface) gives us the pressure we have here, that would also increase towards the middle, at some point it would liquify under the pressure (given that it is at a reasonable temperature since you dont burn up on this trip)

Answer 11

I believe that you would be fried before you know what it really is, but supposing that you have supernatrual powers and can last that long through the heat, I'd say that you are stuck in the center of the earth until you muster enough energy to climb out again. this is because gravity gets stronger the deeper you go into something. Thus, the gravity at the center will be much harder to escape. It is pulling you INWARD, and not rejecting you OUTWARD, so, it is most likely you will be stuck in the center until your supernatrual powers shoots you back out again.