A hole through the earth and its effects?

Assuming earth is solid.
Let's say some alien death ray punched through the center of the earth 10m in diameter.
What'll a person experience if he falls into the hole?

Will he rapidly accelerate to the core, then decelerate on the way out the other side?
Or will he simply be able to walk along the inner wall of the "tube"?

What if the ray blasted through the earth at 90 degrees to the axis of rotation?
Will the centrifugal force purge everything out the tube leaving vacuum, and causing a vortex at the surface where the holes are (air tries to enter the vacuum but forced out by the centrifuge)?

The 10m shaft is sufficently small to ignore the effects the loss of that much matter would have on the Earth's gravity. If it was 1000km, then you'd need to do more complicated maths.

If a person jumped into the shaft, they'd initially accelerate down at 9.8m/s^2, normal surface gravity. As they move closer and closer to the centre, the acceleration gets less and less. When they are half way to the centre, the acceleration is half what is was on the surface, 4.9m/s^2. When they reach the centre, they have a moment of weightlessness, then begin to decelerate as they go up the shaft on the other side of the centre of the Earth. They decelerate in the same way they accelerated. Half way to the surface they are decelerating at 4.9m/s, at the surface they decelerate at 9.8m/s^2.

They'll stop for a moment at the surface, perhaps somewhere in China , then fall back down.

Assuming no air resistence (though there'd have to bew air or they'd die) a person would continue to oscillate in this fashion back and fore forever.

If the shaft was cut at right angles to the Earth's rotation, initially he'd fall as before, but as he does, his rotation about the Earth's centre would mean that to preserve angular momentum he'd crash into one of the walls (takes a spiral trajectory, but the wall stops him). That would remove some of his angular momentum, causing him to fall again. Given some more falling he'd hit the wall again since his angular momentum would still not be zero.

He'd up falling and hitting the wall in intervals until he got to the bottom. Assuming how speed lose from hitting the shaft walls, he'd fly up the other side of the shaft, occasionally having the other side of the shaft bump into him to give him angular momentum. Then when he reaches the top, he'd be rotating with the surface again.

The Earth's rotation isn't fast enough to generate a vacuum, once the air flooded in it would be breathable I think, at least in places.

That is, of course, ignoring the fact the pressure from the Earth would collapse any such tunnel in seconds

Hi mocax,Alphanumeric,

Great question .. great answer.

An ideal opportunity to look at curved space here. Just a little something I'd like to try out if I may..

Considering only a hole through a mass..

As he fell the guy would be in curved space .. this would be why he was falling (except at the very middle when he is just coasting along). Could one view his accleration as generating his own curved space which exactly matches the field he is moving through .. hence (for him) space is flat.

Yes, no , stupid?

-C2.

I suspect this experiment will allow us to examine the teeth and claws of the 'equivalence principle'.

This post has been edited by Confused2 on Jul 24 2006, 11:22 AM

Hi Confused2, AlphaNumeric, mocax et al,

This Gedanken Experiment is the basis of the most important experiment of them all... Gravity Probe B and to the nature of the Gravitational Frame Dragging. This was discussed by me here a while ago and I have a paper that dates from a few decades before... discussing the connection.
Frame Dragging, Frame Dragging : Good Elf
The consideration of frame dragging a mass sphere through space using "external rocket motors". A shaft is cut through to the center of a small dead planet. A freely falling sphere carrying an observer with instruments records the results. Any mass sphere will drag another particle around and displace clocks physically from one point in space to other points without the penalty of clock paradox (or at least as small a penalty as required). A particularly "intractable" problem can be solved using this geometry without providing verification of this idea in itself. The end result is quite interesting and can be used to travel great distances, I mean interstellar distances without space warps. A modification of this principle to include a possible variable mass system in which frame dragging can be used "can do a lot better". The details are still "obscure" though. I described this process even earlier on this site. Unfortunately the pages on this site were damaged and I had to put these points back from my own records.
Einsteins Clock Paradox, Interpretation of the Clock Paradox: Good Elf

The other aspects of the proposed Gedanken Experiment as stated by AlphaNumeric are intriguing and depend on other aspects to be considered to be sure. Spacetime is flat for the freely falling observer in the shaft... the path through space is definitely not a straight line. Keep it simple and have "the Earth" not rotate for the sake of the experiment and for the sake of the luckless observer... Alternatively let the luckless individual fall down a shaft through the rotational poles of a "planetoid"... a dead, airless and cold perfect sphere of uniform density. He would then execute an unattenuated sine wave transverse to the orbital motion of the planetoid in its motion through space. There would not be air in the shaft to slow his fall. Now that is much more interesting than the bruised and battered body of the first "base jumper". If not rotating you can now consider the motions of the "base jumper" with this shaft oriented in the direction of the orbit or perpendicular to the orbit.

As in my first thoughts on this matter and the consequences there is a direct connection between Special and General Relativity as noted originally even though the solution cannot be correctly analyzed using standard theory. Yquantum and I both realize that the consequences of Gravity Probe B are of the utmost importance in this matter. It looks pretty good thus far.

Cheers

The topic has been explored in math, and later in science fiction.

http://www.npl.washington.edu/av/altvw32.html

Gene Roddenbery (of Star Trek fame) wrote another science fiction series (Earth 2?) which was based on travel via such a subway system.

On the other hand, maybe it won't.

LOL

C2.

Molten core would pore out and destroy mankind.

If it was all solid then. He would fall to the centre of the earth or nearest to the centre of the earth if the hole was slightly off centre and die.

If it was perfect situation. The earth being a perfect sphere and gravity uniform throughout the planet then he would fall through the centre of gravity and yo-yo until he would rest at the centre and not die. Friction of the air would slow him untill he rests at centre. He would not be able to get out by walking the sides though someone would have to throw him a rope and pull him up.

This post has been edited by The_Questioner on Jul 24 2006, 09:41 PM

Hi The_Questioner, Confused2, rpenner et al,

Do not fear The_Questioner... I do not think anyone seriously wants to know about really using this method of "transport". The issue of "air" is not of a consequence since you can seal people into containers with "air supplies" and evacuate those tunnels with pumps. I concede the article "Falling through to Pellucidar by John G. Cramer" indicated by rpenner, this involves "shadow matter" or is this dark matter? Of course there has been a controversial proposal that dark matter has been found (axions) and lives in an Italian Physics Lab. Otherwise the Earth is unsuitable for this "experiment".

The full article shows this fella has done the hard yards and tried various approaches and the particles will not go away.

I was more concerned with the consequences of General Relativity and Special Relativity and frame dragging from a theoretical point of view. The question placed by Confused2 is far more interesting. Of course it is up to others to discuss this if they wish.

Cheers

I am not very scientifically astute, but I had the same question as asked (and answered) below. My understanding of the answer is that the lucky fellow who falls all the way down would have a moment of weightlessness. My follow-up question is this:

What happens if that person stops his or her self at the moment of weightlessness? (Ignoring everything such as wind, the rotation of the earth, the obvious problems with findings one's self in the center of the earth), could a person who is able to stop at the center of the earth within this 10 meter hole sit there indefinetly?

Fact is, you'd feel be weightless the whole way down and the whole way back up out hate other side, and through all the cycles of oscillation, as you succumb to earth's gravity.

In the center though, you have a spot where all the gravity cancels itself out. Essentially, there is no gravity. Could you sit there indefinitely? I don't see why not. You could just sit there floating in place...at least until you die. You could also get out by climbing the sides, or as mentioned using a rope. It would be easy at first but get harder the further up you go. And it's a long way up....

Lemme get this straight....the pull of earth's gravity is LESS the closer to the center of the earth, and MORE the further away from earth's center?

So, by that logic Earth's gravity must be VERY VERY strong on the surface of the moon...right? So, if I slipped off the surface of the moon, how fast would I be accelerating towards the earth?

Let's see...halfway to the center the force of gravity is halved. So then twice away from the surface of earth the gravity must be doubled...so on the MOON, the pull of earth's gravity must be on the order of 1 billion ft/sec...is that right?

So, if I slipped off the surface of the moon, I would begin accelerating towards earth at 1 billion feet per second...wouldn't that rip me apart?

So, I guess the moon shot really WAS faked after all, huh? Woooooowwww

The gravitational acceleration you feel increases linearly with distance as you move up from the centre till you get to the Earth's surface. This is because the resultant force on your is due only to the material which is closer to the centre than you. Everything further cancels out. It's known as Newton's Shell Theorem and is easily derivable with a bit of calculs.

Therefore, when you're on the surface, you've the entire Earth closer to the centre than you are, so you feel the full gravity. After that the gravitational force drops off under the well known 1/r^2 relation. Therefore, at the Moon, you have the usual force, which has dropped off like 1/r^2 with r about a quarter of a million miles. In modelling that you can consider the Earth a point mass, because of another theorem, this time due to Gauss.

Either you were attempting to be funny (and failed) or you obviously didn't think about it enough because such a prediction would obviously be experimentally shown to be wrong and Newton's work wouldn't be correct, despite you knowing well, it's a very good model of gravity in the Solar system.

FYI - if you want to see the math for the original question, I put it here:
http://forum.physorg.com/index.php?showtop...ndpost&p=131511

If the gravity is zero in the center of the earth, why does he keep going through to China? Why not just keep slowing down and slowing down until he pretty much stopped at the center after a brief osculation?

in this scenario the centre of the earth has no gravity. gravity is caused by mass not the centre of the mass.

he keeps going through to china because of momentum.

standing at one end there is more mass below him so this drags him down, as he moves through the shaft the amount of mass around him shifts ie at the centre it is evenly distributed around him, so there is an equal amount of pulling in all directions. as he moves past the centre and to the other side the amount of mass around him changes from in front of him to behind him. this causes the oscillation you have described and the eventual suspension in the centre.