# A hypothetical question about gravity

1. Jun 2, 2012

### schnorbitz

I thought of a question and its been causing some debate with my collegues. Its completely hypothetical and possibly ridiculous but i'm looking for somebody's more educated take on it.

Here goes:

Say you could theoritically drill a large hole between the poles of the Earth, large enough that contact friction wouldn't be an issue and lined with some super insulator as to rule out the heat element. What would happen if you jumped down this hole? presumably you wouldnt emerge at the other side, shooting out the ground! What follows when you reach the centre?

2. Jun 2, 2012

### phinds

There is a dampened (by air friction) oscillation up and down the hole until eventually you settle in at the center of the earth and die of starvation.

3. Jun 2, 2012

### A.T.

You would emerge at the other side, at the same speed you jumped in, ignoring air resistance. With air resistance you end up at the center after going back and forth for a while.

4. Jun 3, 2012

### shreyakmath

In this hypothetical situation, you will emerge out of the other side.
You may also cause some serious magnetic disturbances while passing through the core of earth.

5. Jun 3, 2012

### Staff: Mentor

Why? A human is tiny, and usually not charged in a significant way. The tunnel itself would need an incredible strength to keep in the same position for years, or would just move with the surrounding material. But that does not depend on any objects falling trough it.

The trip would need 42 minutes without air resistance and you would reach the other side with ~0 speed (depends a bit on the surface levels on both ends).

6. Jun 3, 2012

7. Jun 3, 2012

### Kulen

Go to youtube and copy this after com:

/watch?v=21tR5wyTeSY&feature=plcp

Sorry I cant post normal link because forum rules are you have to have at least 10 posts.

This guy has some more videos where he answers questions like that.

8. Jun 3, 2012

### poco9964

I doubt you could come out the other side. I lack the mathematical skills to give you the relevant equations, so I will explain why as best I can.

To my limited understanding terminal velocity is gravity pulling on mass + friction.
The gravity in the centre of the Earth is zero due to a cancellation effect.
The closer you got to the Earth's centre would reduce the amount of gravity being excreted on your mass. That would slow your terminal velocity, deceasing due to a decrease in gravity excreted on your mass. If you passed the centre you would be travelling at a lot lower terminal velocity than at a few miles in to your journey.

This would then leave the question of if you had enough velocity to overcome the pulling effect that would be exerted on you as you pass the centre. However that would be just as plausible as a marble placed in the centre being able to gather enough energy to break free from the friction placed on it without any cause for initial inertia.

Think of it this way, it takes longer to fall on the moon than it does here on Earth.

BTW, if anyone knows I am wrong, then please correct me as I am only an armchair physicist who feels massively out of his comfort zone on this forum.

9. Jun 3, 2012

### A.T.

Here the video mentioned by Kulen:

10. Jun 3, 2012

Decrease in gravity does not equal decrease in velocity. In fact your acceleration would decrease but as long as it's greater than zero you would continue to gain speed (or stay at terminal velocity).

11. Jun 3, 2012

### A.T.

It effectively does, when you are traveling at terminal velocity.

That terminal velocity that you stay at goes to zero towards the center. So depending on your mass/drag ratio you might even hardly make through the center.

A normal human will reach his terminal velocity rather quickly on the first few hundred meters. After that he will start to slow down as gravity drops, assuming uniform mass distribution. In the real Earth the slow down would begin on entering the outer core:
http://en.wikipedia.org/wiki/File:EarthGravityPREM.jpg

12. Jun 3, 2012

### poco9964

Hello A.T

I watched the video, and I have queried the answer to the physicist. Still no reply as of yet. I am a little unsure as to why you brought it up as you later seem to go on and agree with me?

This is really my point, because you would have long reached terminal velocity. The only out come is, you would slowly decrease terminal speed and come to a nice stop. I fail to see where any increase in speed can be gained to then go against gravity that will always increase in force pulling you back the further you get away from the zero point.

13. Jun 3, 2012

### Aero51

To solve this problem will will have to integrate the gravitational field around yourself as you fall (which will result in a decrease in acceleration due to gravity as you fall) minus the drag associated with the direction of your decent (....or perhaps ascent?). This translated to a somewhat complicated differential equation. I would guess that you will fall just slightly past the earths core then oscillate.

14. Jun 3, 2012

### A.T.

I just posted it for convenience because Kulen couldn't post links. The vacuum part of it is ok. But I agree with you that the damping in the lossy part is way underestimated.

Last edited: Jun 3, 2012
15. Jun 3, 2012

### A.T.

Anther thing there is that the air would become denser towards the center causing more drag. So even for constant g (like in the lower mantle area) you would already start to slow down.

16. Jun 3, 2012

### Ken G

Incidentally, if we assume the Earth has a constant density (not a terrible assumption, not good either), then this problem is exactly the same as a mass on a spring in some kind of viscous fluid (to get the resistance). The force from mass inside the radius of the object will be proportional to radius, just like a spring force is proportional to displacement from equilibrium. The point is well taken that usually terminal velocity is way less than the speed you would acquire in the absence of air resistance, so of the two easy ways of doing it (either neglect air resistance, or embrace air resistance and say the velocity is always equal the terminal speed), the latter should be by far the more accurate, but does suffer one strange aspect-- it doesn't oscillate, it takes an infinite time to fall the first time! So you might not get any oscillation at all, nor even ever get to the center, but in practical terms, that would still seem like coming to the center and reaching a "nice stop."

Last edited: Jun 3, 2012
17. Jun 3, 2012

### Aero51

That is not true at all. The density of the air changes with altitude due to hydrostatics which is essentially an integration density WRT height. This assumes that gravity is acting downward. This is not the case once you go below the surface of the earth. The air may actually circulate at the core (similar to convection currents in boiling water), which will result in a rise in drag because of the relative velocity of the air and the (maybe) falling object in question.

18. Jun 3, 2012

### Aero51

Actually, thinking about this problem in terms of fluid mechanics is quite interesting. I'm thinking that the air near the core would act like a source in potential flow. HMMMMMM......

19. Jun 3, 2012

### Ken G

I'm not sure what you mean here-- gravity would still act downward, and the air would certainly be more dense at the center. We might want to imagine that the hole is much wider than the falling object, so the air can move around it, or the situation might change a lot.

20. Jun 3, 2012

### Aero51

I meant to say it has an upwards component too. Yes the density will increase but I doubt it would be much at all because there probably isnt enough air in the atmosphere to fill the hole if its wide enough.

21. Jun 3, 2012

### Subductionzon

Of course to do this you can only do this if you ignore certain physical laws. If it was a hole through the actual Earth your acceleration would increase for the first half of the trip until you hit the core/mantle boundary at which point you would be accelerating at about 10.8 m/sec^2 if there is a vacuum in the hole.

Now if there is air in the tube the pressure will go up until the air is no longer a gas, it would be a supercritical fluid. If the hole was man sized it will not hold a significant fraction of the Earth's gravity.

So let's put magic baffles in the tube. We already have magic sides that keep the heat out and stand up to amazing pressures so a little more magic can't hurt. You will fall at terminal velocity the whole trip down and never quite reach the center.

22. Jun 4, 2012

### Ken G

But it doesn't, all the force from mass outside the radius of the object will add to zero. You only need to look at the mass of the sphere inside that radius, and ignore the rest.
The hole doesn't need to be kilometers wide, so there's no need to worry about that.

23. Jun 4, 2012

### Ken G

So you are including actual density variations within the Earth, we'll probably have to take your word for that calculation, given your handle!
Yes, the hole would have to be magically held open, or pressure would close it immediately. I agree you would probably never formally reach the center, but in practical terms, you probably would because the approach is exponential in time. It might take quite a while though, you'd probably starve to death waiting!

24. Jun 4, 2012

### A.T.

Would the pressure really be enough to make air liquid at the center? I guess it depends on the temperature. But let's assume the tunnel is well insulated.

Anyway, gas or liquid, it would be denser.

Last edited: Jun 4, 2012
25. Jun 4, 2012

### Aero51

The acceleration of gravity will decrease (approaching zero) as you move towards the core. The net contribution will always face the center of the earth but there will be a component due to the mass behind the object that will account for the decrease in g.