Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 12/03/2012 08:50:03
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Adam McGuirk asked the Naked Scientists:
If you could dig a hole straight through the Earth and decided to jump into the hole, what would happen when you reached the centre point?
What do you think?
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1. You would burn up - it's quite hot down there. But, if you were to ignore heat...
2. You would hit the side of the hole. At the equator you are doing at 1600kmph laterally, you would end up going faster than the hole... But if you were to dig pole to pole...
3. Those two provisos aside; when you reached the centre you would be travelling very quickly - enough to get you all the way to the other side of the earth. As you passed the centre you would start slowing down again, and (barring air resistance) you would slow down to a stop just as you appeared on the other side of the world.
4. You would then oscillate back and forward - in an ideal setup with no losses due to friction - forever; each time reaching the surface, stopping and then falling back down to the other side of the world.
BTW Newton calculated how long it would take! And even more amazing is that the theoretical time (ignore bumps and friction) is exactly the same for all tunnels through the earth - even those that doe not go through the centre. The shallow tunnels are shorter, but you get a slower top speed.
There is a wikipage here (http://en.wikipedia.org/wiki/Gravity_train)
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A there and back trip would take the same time as a satellite orbiting at ground level, if you held your arms out to create some friction you would stop at the centre and just float.
The transit time depends only on the density of the planet not its size.
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that would be one heck of a fairground ride.
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There is a wikipage here (http://en.wikipedia.org/wiki/Gravity_train)
Qi item on YouTube here (https://www.youtube.com/watch?v=pv8Z5N8hqDI&#t=2m15s)
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A jojo, with a slight twist methinks :)
You have those 'imaginary forces' to consider too, as the Coriolis force
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A jojo, with a slight twist methinks :)
You have those 'imaginary forces' to consider too, as the Coriolis force
a string moreso than a spring?
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alphbetically, the p comes be4 the t
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Adam McGuirk asked the Naked Scientists:
If you could dig a hole straight through the Earth and decided to jump into the hole, what would happen when you reached the centre point?
What do you think?
hi, im glas i found this question, years ago , arround 2004 i think i asked myself this exact question. Adding to it:
what is gravity? at the centre of the earth (im in a heat proof tunnel :)) does the earth's mass: shrink me or stretch me.
once again, i was about to ask your question on this forum, and was amazed to find it already asked :)
what i learned from the question is: that there is actually no exact understanding og what gravity actually is in phisics, so the question remains valid and i think unanswered.
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Adam McGuirk asked the Naked Scientists:
If you could dig a hole straight through the Earth and decided to jump into the hole, what would happen when you reached the centre point?
What do you think?
hi, im glas i found this question, years ago , arround 2004 i think i asked myself this exact question. Adding to it:
what is gravity? at the centre of the earth (im in a heat proof tunnel :)) does the earth's mass: shrink me or stretch me.
once again, i was about to ask your question on this forum, and was amazed to find it already asked :)
what i learned from the question is: that there is actually no exact understanding og what gravity actually is in phisics, so the question remains valid and i think unanswered.
in the gravitational centre of the sphere i think you woul suddenly stop (forever) since the force that was pulling you lets say from south pole towards north pole, in the exact gravitational centre of the sphere would suddenly transform into forces that either pull you appart from centere in all directions equally strong (hense imemediate stop, full stop, forever) << OR ? >> posh towards the centre itself (shrink you) from all directions.
i think there is no answer to A OR B? since gravity isnt defined at all. and this question is the important one:
if now we imagine that we could freeze time while at the exact ventre of the sphere: i bet 50% of you would vote: the sphere's mass is pulling you apart, and 50% would vote its pushing you in (shrinking you)
pull or shrink?
;)
what IS gravity?
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There is no net force from the body and no stress on the body if it is at the centre of gravity of that body. It is easily provable (by integrating the equations) that the gravitational acceleration (force) inside a massive uniform thick spherical shell is zero at all points inside the shell. Outside of the shell it behaves as if all the mass in the shell was concentrated at the centre of the sphere and when you move through the shell from the outside to the inside the gravitational acceleration (force) falls linearly from the value outside of the shell to zero linearly.
There may be slight deviations from this for non uniform, not precisely spherical and rotating bodies but there is always a centre of gravity where the forces are zero.
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As an aside there was a science fiction story of a planet with a thin crust a large liquid core containing two heavy bodies orbiting each other inside the core. The local gravitational field was then continually varying in magnitude and direction with interesting effects. Notably it was possible to move around in a wheeled vehicle on the reasonably flat surface of the planet by waiting until it was downhill in the direction you wanted to go letting off the brakes and coasting but putting the brakes back on again and staying where you are when it was uphill in the direction you wanted to travel!
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There is no net force from the body and no stress on the body if it is at the centre of gravity of that body. It is easily provable (by integrating the equations) that the gravitational acceleration (force) inside a massive uniform thick spherical shell is zero at all points inside the shell. Outside of the shell it behaves as if all the mass in the shell was concentrated at the centre of the sphere and when you move through the shell from the outside to the inside the gravitational acceleration (force) falls linearly from the value outside of the shell to zero linearly.
There may be slight deviations from this for non uniform, not precisely spherical and rotating bodies but there is always a centre of gravity where the forces are zero.
thank you,
this would mean i would be "stretched" in all cases - or not? I gather that AT the centre the G=0, on my trip from North to South id be pulled towards the centre with F(m to the South) and "away" from the centre with F(m to the North), this F becomming smaller as i further travel to the centre and finnaly 0 in the centre.
id assume, that if the G force didnt drop while traveling closer to the centre, but accumulate (or even stay the same), the body would collapse into itself, such as in a black hole. in such a case only, i would be "squeezed" in?
Best
W
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Inside the cavity there are no forces on you due to the gravitating sphere. You would not be stretched. The same thing applies even at the centre of a black hole at the instant the event horizon forms. There is always a still and forceless centre however small it is.
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2. You would hit the side of the hole. At the equator you are doing at 1600kmph laterally, you would end up going faster than the hole... But if you were to dig pole to pole...
If digging equator to equator, you would have to design your tunnel with a curve due to the Coriolis effect (http://en.wikipedia.org/wiki/Coriolis_effect).
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Soul Surfer
I find it hard to believe, if the hollow sphere was real thin walled and I was real long, not very realistic surely but would there still be no stretching ?
What I visualise is replacing the hollow sphere by its one dimensional equivalent i.e. two separated masses with a long me in between would I not be stretched then ?
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Syhprum - if my maths is correct you cannot directly lower the dimensions; without redoing the maths I think the integration works because you are dealing with a shell in 3d with a inverse square law. The size of the interior object does not matter - at every point within the shell there is no net force. ie each subdivision of your long test subject will all feel the same attraction that is say none - therefore there is no variance in attraction (or direction of attraction) and no stretching or skewing
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Thank for the demolition of my hypophosis I have learnt not to argue with maths.
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Thank for the demolition of my hypophosis I have learnt not to argue with maths.
Now you have said that I feel honour bound to check. I am certain about the no stretching - but the lower dimensional model I am not so certain is incorrect. My maths homework has been set... :o
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http://www.yale.edu/phys180/lecture_notes/180_Lect_31/sld007.htm
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It would appear from the graph that a stationary long body at the centre would be compressed.
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It would appear from the graph that a stationary long body at the centre would be compressed.
In a tunnel - yes. in a shell - no
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For an "infinite" uniform cylindrical gravitating body (or a very long one nowhere near the end or possibly a large torus stabilised by rotation) there is no net force. But I am not sure if it is a stable equilibrium and it might tend to break down int individual blobs. It is interesting to note that in this case the gravitational field fall off as you leave the surface of the cylinder is not an inverse square law but an inverse first power law because of the dimensional reduction.
To take this one step further the gravitational field from an "infinite" massive plane does not fall off at all but is a constant.
This could have an effect on the models of the real collapse of material inside a rotating black hole towards the hypothetical ring singularity.
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The whole thing sounds like a shell game to me.
Meanwhile, I'm trying to abolish "microgravity". Do I get any help? Not blinking likely!
"Ho no Mr Geezer. We're much too busy solving real problems to worry about silly stuff like that."
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How about abolishing macro gravity like the useful shields do in Sci Fi stories.
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Earth is a lousy place to dig a tunnel through. It's not possible, so why not pick a planet where it is possible. Pick a planet whose core is cold and solid and strong enough to support its own weight without collapsing the tunnel. First consider a planet with no atmosphere and hypothesize that it is as large and as dense as Earth but made of a material like diamond which is strong enough not to collapse the tunnel. To simplify the math, assume it has constant density, despite the compression toward the center. Also assume that the planet does not rotate.
In that oversimplified case, the strength of gravity inside will be proportional to the distance from the center; outside, the gravity will decrease as the inverse square of distance from the center. An object dropped into the tunnel will start accelerating downward at 1 g, and the acceleration will decrease to zero at the center; it will decelerate toward the opposite side, reaching zero velocity at the top. The speed as it passes the center will be the same as the orbital speed of a satellite at the surface, about 8 km/s. It will continue to oscillate back and forth between the two ends. The period of this oscillation is a bit less than the orbital period of a low earth orbit satellite; about 87 minutes.
Now, if you add an atmosphere, the situation is very different. With one Earth atmosphere pressure at the surface, the pressure will increase dramatically as you fall in. It's about 100 kPa at the surface and 200 kPa at a depth of about 10 km. It increases exponentially, so by the time you reach the center (3180 km) it might be something like 10,000 atmospheres. That's just a wild guess. The formulas break down because, at some point, the atmosphere becomes liquid. As the pressure increases, the air becomes more viscous, so you quickly reach terminal velocity of about 195 km/hr, then you decelerate until your are barely moving. You can expect the air to get hotter as the pressure increases, so you eventually burst into flames and your ashes slowly drift toward the center, where they remain forever.
If your planet is rotating, you better drill your hole from pole to pole so you won't drag against the sides of the tunnel.