A hypothetical question about gravity

In summary, the conversation discusses the hypothetical scenario of drilling a large hole between the poles of the Earth and jumping down it. The debate revolves around what would happen during the fall, including potential emergence on the other side, effects on gravity and velocity, and the possibility of reaching the center of the Earth. The conversation also mentions a YouTube video with more information on similar topics.
  • #1
schnorbitz
1
0
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 wouldn't emerge at the other side, shooting out the ground! What follows when you reach the centre?
 
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  • #2
schnorbitz said:
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 wouldn't emerge at the other side, shooting out the ground! What follows when you reach the centre?

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
schnorbitz said:
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 wouldn't emerge at the other side, shooting out the ground!
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
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
You may also cause some serious magnetic disturbances while passing through the core of earth.
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).
 
  • #7
Go to youtube and copy this after com:

/watch?v=21tR5wyTeSY&feature=plcp

Sorry I can't 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
schnorbitz said:
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 wouldn't emerge at the other side, shooting out the ground! What follows when you reach the centre?

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 traveling at a lot lower terminal velocity than at a few miles into 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
Here the video mentioned by Kulen:

https://www.youtube.com/watch?v=21tR5wyTeSY
 
  • #10
poco9964 said:
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 traveling at a lot lower terminal velocity than at a few miles into your journey.
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
Dead Boss said:
Decrease in gravity does not equal decrease in velocity.
It effectively does, when you are traveling at terminal velocity.

Dead Boss said:
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).
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
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?

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.

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
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 Earth's core then oscillate.
 
  • #14
poco9964 said:
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?
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.
 
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  • #15
Aero51 said:
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.
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
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."
 
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  • #17
the air would become denser towards the center causing more drag
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
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
Aero51 said:
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.
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
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 isn't enough air in the atmosphere to fill the hole if its wide enough.
 
  • #21
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
Aero51 said:
I meant to say it has an upwards component too.
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.
Yes the density will increase but I doubt it would be much at all because there probably isn't enough air in the atmosphere to fill the hole if its wide enough.
The hole doesn't need to be kilometers wide, so there's no need to worry about that.
 
  • #23
Subductionzon said:
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.
So you are including actual density variations within the Earth, we'll probably have to take your word for that calculation, given your handle!
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.
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
Subductionzon said:
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.
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.
 
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  • #25
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.
 
  • #26
Aero51 said:
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.
But that's not a very useful way to think about what is going on there. The force decreases simply because there is less mass in the sphere within the radius of the falling body. There is no net contribution from the mass outside that sphere, so the force should not be thought of as falling off due to any contribution coming from out there.
 
  • #27
A.T. said:
Would the pressure really be enough to make air liquid at the center?
No, not if we are magically holding the hole open. Then the pressure of the air would just come from the weight of the air in the shaft, not from the weight of the Earth, and it would not be any kind of huge pressure.
 
  • #28
A.T. said:
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.

I see no reason to assume there would even be these kind of pressure present in the hole. Mainly because all the mass that would have caused that pressure would have been removed when making the hole. The only pressure would be air, it would cause a displacement that could have catastrophic effects on the crust. It may effect the layers of the atmospheres that protects us from harmful UV rays. Ignoring that, I am not even sure if the air could be drawn to the centre. Mainly because its mass its significantly less than the object that is falling through it. The point at which air could resist the gravity and reach a state of equilibrium would be a lot higher up the hole than we could fall. I actually think it would create a void in the centre, that closely resembles space. And if we managed to reach it, it would be like being in a membrane that you have no friction to stop you bouncing of the sides, and not enough inertia to ever break free again. Well that is if you do not go down with something that packs the punch of a soyuz rocket. But fits in your pocket.
 
  • #29
Ken G said:
But that's not a very useful way to think about what is going on there. The force decreases simply because there is less mass in the sphere within the radius of the falling body. There is no net contribution from the mass outside that sphere, so the force should not be thought of as falling off due to any contribution coming from out there.

Now that has got my mind thinking.

If I reached a point where the mass in the sphere above me was greater than that what was below me. Why does this have no effect would on my mass, and why would the mass above me now not become the greater force?

Sorry if that is a silly question.
 
  • #30
poco9964 said:
The only pressure would be air,
But a lot of it. 1 bar is from the 100km column above surface at approx. constant g. In the tunnel center the column would be 63 times higher, however at decreasing g. My question was if that is enough pressure to make air liquid.

poco9964 said:
It may effect the layers of the atmospheres that protects us from harmful UV rays.
If you don't make the tunnel to wide, I doubt it. The polar bears could reach the Antarctic and eat all the penguins.

poco9964 said:
Ignoring that, I am not even sure if the air could be drawn to the centre. Mainly because its mass its significantly less than the object that is falling through it. The point at which air could resist the gravity and reach a state of equilibrium would be a lot higher up the hole than we could fall. I actually think it would create a void in the centre, that closely resembles space.
What do you mean? What should stop the air from falling to the center?
 
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  • #31
poco9964 said:
Now that has got my mind thinking.

If I reached a point where the mass in the sphere above me was greater than that what was below me. Why does this have no effect would on my mass, and why would the mass above me now not become the greater force?

Sorry if that is a silly question.

The mass "above you" in terms of a spherical shell has no effect on you. The gravity of it cancels itself.

The mass "above you" in terms of a sphere section would only become greater if you pass the center. Then gravity is reversed.
 
  • #32
A.T. said:
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.
Close to the surface, air density doubles every ~8km. This would give conditions similar to the critical point (~3,5MPa, 126K for nitrogen) already 40km below the surface. Give or take a factor of 2, the air would be supercritical in most of the tunnel unless you evacuate it in some way.
 
  • #33
A.T. and Subductionzon have it right. Gravitational acceleration inside the Earth reaches a global max at the core mantle boundary and then drops to zero per the Preliminary Reference Earth Model.

Reference: Dziewonski & Anderson, Preliminary reference Earth model, Physics of the Earth and Planetary Interiors, 25:4 (1981)
DOI: 10.1016/0031-9201(81)90046-7
Tabular presentation: http://geophysics.ou.edu/solid_earth/prem.html [Broken]
Paper: http://mh-gps-p1.caltech.edu/uploads/File/People/dla/DLApepi81.pdf [Broken]

A simple model of gravitational acceleration inside the Earth is that gravitation remains constant at 10 m/s2 from the surface to halfway to the center and then drops linearly from that point inward. This is much more amenable to analysis than is the PREM but still retains the key feature that gravitational acceleration remains high in the crust and mantle.

What happens to air inside the magical tunnel depends on temperature. Assuming this simple model, ideal gas conditions, hydrostatic equilibrium, and a constant temperature of 20 C throughout (magical walls!) would mean an absolutely ridiculously high pressure at the center of 5.5*10493 atmospheres. Assuming hydrostatic equilibrium and adiabatic conditions would mean ridiculously high pressure and temperature at the center.
 
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  • #34
D H said:
would mean an absolutely ridiculously high pressure at the center of 5.5*10493 atmospheres.
I guess this ridiculous result is due to the assumption that the gas can be compressed without limits, so that density increases steadily?

The molecular hydrogen atmosphere of Jupiter is thicker than one Earth radius. Gravity is in the same order of magnitude in that region. The pressure below that atmosphere is estimated to be 200 GPa. Which is much, but nowhere close to 10493 atmospheres.

http://en.wikipedia.org/wiki/Jupiter
 
  • #35
A.T. said:
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.

Not liquid, that is impossible. Air is far above the critical temperature of the various gases that are in it. It would be as I said a supercritical fluid. I did the math once before when trying to calculate the density of the air using the Ideal Gas Law. I got a ridiculous solution that showed me the law broke down at those pressures.

Using the ideal gas law you don't have a gas column of constant density. You will have one that will continually increase in density. Eventually you are not dealing with a gas anymore. Since the force of gravity goes up slightly for the first half of your journey you can make the problem easier by treating it as a constant for that distance. It should double in density over a constant distance. At sea level the pressure drops off to half at 18,000 feet or 5,500 meters. Going down half way you would have 280 of these intervals. Or the density of the air, if the Ideal Gas Law held up would be 2^280 times that at the surface. This amount would obviously be in error so there is no use in using the Ideal Gas Law. Therefore the need of our magical baffles to keep the air at a reasonable pressure.
 
<h2>1. How does gravity work?</h2><p>Gravity is a natural phenomenon by which all objects with mass are brought towards each other. It is the force that keeps planets in orbit around the sun and causes objects to fall towards the ground.</p><h2>2. What is the difference between mass and weight in relation to gravity?</h2><p>Mass is a measure of the amount of matter an object contains, while weight is a measure of the force of gravity acting on an object. The more mass an object has, the greater the force of gravity it experiences.</p><h2>3. Can gravity be turned off or reversed?</h2><p>No, gravity is a fundamental force of nature and cannot be turned off or reversed. However, its effects can be counteracted by other forces such as lift or thrust.</p><h2>4. Does gravity affect all objects equally?</h2><p>Yes, gravity affects all objects with mass equally. However, the effects of gravity can be more noticeable on larger objects with more mass, such as planets and stars.</p><h2>5. How does gravity change with distance?</h2><p>Gravity follows an inverse square law, which means that the force of gravity decreases as the distance between two objects increases. This means that the farther away an object is from a source of gravity, the weaker the force of gravity it experiences.</p>

1. How does gravity work?

Gravity is a natural phenomenon by which all objects with mass are brought towards each other. It is the force that keeps planets in orbit around the sun and causes objects to fall towards the ground.

2. What is the difference between mass and weight in relation to gravity?

Mass is a measure of the amount of matter an object contains, while weight is a measure of the force of gravity acting on an object. The more mass an object has, the greater the force of gravity it experiences.

3. Can gravity be turned off or reversed?

No, gravity is a fundamental force of nature and cannot be turned off or reversed. However, its effects can be counteracted by other forces such as lift or thrust.

4. Does gravity affect all objects equally?

Yes, gravity affects all objects with mass equally. However, the effects of gravity can be more noticeable on larger objects with more mass, such as planets and stars.

5. How does gravity change with distance?

Gravity follows an inverse square law, which means that the force of gravity decreases as the distance between two objects increases. This means that the farther away an object is from a source of gravity, the weaker the force of gravity it experiences.

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