What you are still refusing to understand is that these forces are symmetrical and cancel each other out.
Warning: this kind of abuse of the word “theory” is one of the ten warning signs of invincible ignorance.
You’ve been told twice now.
I suppose you think the word “shell” is there just for decoration?
What the bloody hell does that have to do with anything?
So the mass to the “sides” of the subject body, being equidistant in radius and equal in mass, would act the same from all sides 360 degrees and hold the body in alignment to the axis through which it is falling. The only way it could act otherwise would be if the axis was offset from exact center. 
Pendulums on clocks are law, fully calculable and predictable as a harmonic frequency, the contention that a body falling through the Earth and acting like a pendulum is still a mere theory. I abused nothing.
But now I understand (see above).
I assumed the shell to be hypothetical in nature as it was stated that it had no mass and thus no gravity. ie: it isn’t really there but noted for purposes of discussion (a “shell” as opposed to a shell). A shell of any thickness, even infinitesimal, would have to have some mass and thus some gravity; would it not?
If the shell is 400 miles thick and has a hollow core of 200 miles diameter, is the gravity anywhere within the hollow structure still zero? That was what was stated by markci:
Would that statement be true under those circumstances? Would a body within that hollow area simply bounce around as though the shell were a capsule in space at “zero” gravity? 
By the way, he did make an incorrect assumption in bringing the hollow shell into play. He stated:
There was no hollow shell above me. The Earth is the model so no hollow shell exists. There is merely solid mass “above” and solid mass “below” with the exception of the tunnel through which the body is falling. As the body falls through the tunnel, the mass “above” gets greater and the mass “below” becomes smaller; does it not?
I’m going to state this as clearly as I can; but it is still going to sound convoluted. So here goes:
I guess my problem is seeing the mass as surrounding the body and acting upon it as though the body is always at some point where the gravitational forces are generated relative to the amount of mass in any given direction; instead of the mass acting as a whole regardless of the position of the body within it. ie: if the tunnel were to miss center by 2 feet, at the center, the body would still fall “straight” down until it got to the center and then would be thrown against the wall of the tunnel as it passed by the center of gravity.
I wanted to know if the magnetic axis of the Earth, (magnetic North and magnetic South) being out of alignment with the rotational axis would have any effect on the falling body. Having the tunnel through the rotational axis, as brought up by jezzaOZ would negate the rotational problems noted but what, if any, effect would the offset of the gravitational axis have on the body?
If there is any effect then the problem becomes an impossibility. Either the tunnel has to address the rotational effect; or it has to address the gravitational effect (if any).
I pose these questions because I want to know, not to be a pain in the ass. There are great minds here and, while it may take a while for me to “get it”, the questions are real, not contrived to annoy. For those who are annoyed, I apologize.
jimpeel yess anything inside a hollow spherical shell will not feel the graviational effects from the shell as they exactly cancel out, this applies to any location within the shell.
When they mention the North Pole and the South Pole, they are talking about the rotational poles, not the magnetic poles.
I am aware of this; but this is not what I mean.
The North Pole and South Pole are the points on the Earth where the rotation of the planet takes place. They are also the points on the Earth where no matter which way one faces they are facing South (at the North Pole) or North (at the South Pole). They are, however, not magnetic North and Magnetic South or those points on the Earth where a compass points from any other point on the Earth. In addition … they move!!! – DAILY!!! :eek:
Here is a gif of the (approximate) location of Magnetic North.
http://www.geolab.nrcan.gc.ca/geomag/images/nmplocation.gif
See http://www.geolab.nrcan.gc.ca/geomag/northpole_e.shtml for the following:
(I hope this all come out as there is no “edit” function on these boards) 
You must also contend with this little anomaly as well:
From: http://www.geolab.nrcan.gc.ca/geomag/daily_mvt_nmp_e.shtml
http://www.geolab.nrcan.gc.ca/geomag/images/nmpoval2001d.gif
Now, to continue, is a body falling through the center of the Earth from the North Pole to the South Pole in an a line coincident to the exact axis of rotation going to be affected by the fact that the Magnetic Poles of the Earth are not coincident to the rotational axis? Absent the subject body holding a magnet in his hand, that is. 
Preview Replay would handle that.
No, we’re assuming that the falling body is not magnetized and thus will not be affected by the magnetic poles. For a person magnetism would only have a nominal effect on the scenario.
Thank you.
RM Mentock
:smack: Shoulda thought of that. Also shoulda read the image at the bottom of the page that says image code is off. Thanks.
MC Master of Ceremonies
So the elemental chemical makeup of the body, including Iron, would have no effect? The falling body exists, for all intents and purposes, in zero gravity during the freefall – assuming a perfect vacuum as well – does it not? Like the Vomit Comet, as it were.
It would have almost no effect. The amount of gravity and therfore the accelration of the body would get less and less until it reached the centre where it would be zero (and it’s velocity would be a maximum), which is exactly analgous to simple harmonic motion (simlairly it would have the maxmium accelration and miniumum velocity at the surface). Of course this is not considering friction etc., but this would merely change it’s motion to dampened harmonic motion which is the same type of motion experinced by realistic pendula.
Okay, the perfect tunnel, through the perfect rotational axis, through the perfect center of the Earth; would the “almost no effect” be enough of an effect to pull the body against the wall of the tunnel? Perhaps not at the “top” of the fall when gravity is at its greatest and the velocity at its least, but at the point of equilibrium, or “below”, perhaps? Of course, the magnetic flux would also be lessened that deep in the Earth as well – considering it as a bar magnet per se.
No. Everything’s perfect. Besides, if the body were pulled against the wall, it’s perfectly frictionless.
jimpeel, you really don’t understand what a physicist means by the term “theory”. You can’t say that the behaviour of an object falling through a sphere is a “mere theory”; a theory is never “mere”. “Theory” is one of the highest levels a scientific idea can reach. And to cast doubt on a theory, you need to do more than just say “I don’t believe it”. There are only a few ways you can cast doubt on a theory: First, you can perform the experiment, and see if the results agree with the theory. This is the best method, but as you rightly point out, nobody has dropped objects thorough the Earth, nor is anyone likely to any time soon, so we’ll forget about that one. Second, you can come up with some factors not taken into account by an existing theory, and show why those factors are relevant. You have not done so: You’ve pointed out that gravity is three-dimensional, and everyone here has already taken that into account. You’ve pointed out that masses in all directions from an object will attract it, and we’ve already taken that into account, too. And you’ve pointed out that the Earth has a magnetic field, too, but that’s irrelevant, since we’re talking about gravity, not magnetism.
As for the spherical shell, you’re the only person who said that the shell is massless. The fact is, if you take a spherical shell of any mass, and any thickness, then an object anywhere inside the hollow space inside the shell will feel exactly zero gravitational force from the shell. The proof of this requires calculus, but I can give you the basic idea easily enough. If you’re off the center of the sphere, then on one side of you, the shell is nearer, but there’s more of the shell on the other side of you. Gravitational force depends both on the mass of the attracting object and on its distance from you, and it depends on both in just such a way that the gravitational force from opposite sides exactly cancels out.
Now, why a shell is relevant: Yes, the Earth is a solid, non-hollow sphere. But you can split a sphere up into an outer shell with some thickness, and an inner sphere that exactly fills up the inside of that shell. So, if you’re, say, halfway down to the center of the Earth, then there’s a shell of matter from r/2 to r above you, and a sphere of matter from 0 to r/2 below you. As discussed above, the gravity from the sphere above you exactly cancels out, so the only gravity you feel is the gravity from the sphere below you.
Another way to show that you can’t stop at the center is to use conservation of energy. When you’re standing on the surface before you fall in, you’re not moving, so you have zero kinetic energy. But you have some height above the center, so you do have some gravitational potential energy. Now, when you reach the center, you have less potential energy, but you still need to have the same total amount of energy, so you need to have more kinetic energy than you had at the surface. Which means you still have to be moving.
My point with the Earth’s magnetic field is that it being offset from the rotational axis through the poles MIGHT have some effect on a falling body because that falling body is at zero gravity relative to everything but the force pulling it downward.
Now this is where the magnetic field comes to play. The human body contains iron in sulphated and phosphated forms. It is, however, still iron and is still magnetic.
In addition, addressing the explaination of MRI at http://www.cis.rit.edu/htbooks/mri/chap-1/chap-1.htm one finds that there are other levels of magnetic fields being produced within the human body. This is discussed further at: http://www.cis.rit.edu/htbooks/mri/chap-3/chap-3.htm#3.3 This is why MRI works.
It is impossible that these fields, in a zero gravity environment, cannot be addressed. There has to be some effect; and is there any possi or probability that the interaction of the magnetic properties of the body and the Earth’s magnetic field would send the subject body, falling at zero gravity through a vacuum, into the wall of the tunnel?
RM Mentock caught me in the use of the word “perfect” and, in a perfect tunnel he would be totally correct. No friction, no atmosphere. Just the falling body, gravity, acceleration and velocity. In that world, the body could slide up and down the walls of the tunnel with impunity and my argument is moot.
But even in that world, the magnetic properties of the Earth and the subject body cannot be ignored; regardless of how small they may be.
What I said is that I thought the shell was hypothetical to the excercise. I now understand otherwise.
I posed this scenario
and MC Master of Ceremonies told me "Yes"and I now understand why by his explaination.
Now this is significant and thank you, thank you, thank you.
My mind got wrapped around the term “hollow” and it was a point of confusion for me.
So as the subject body falls through the tunnel, there is a shperical line of demarcation between the mass “above” it and the mass “below” it that follows the body, and gets smaller, as it “descends”. The mass “above” the body acts the same as if it were a hollow shell. As the body approaches the other side of the sphere it gets equally as far away from the point of departure. The only thing that continues to act upon the body is the mass below as the mass beyond the opposite spherical line of demarcartion is negated by the mass “above”.
Stands to reason now the cobwebs are dusted out. My original contention was based upon changing masses about the body and why they might cause the body to simply stop at the center. That was, of course, before the shell explaination shot it to Hell. Thanks.
Still can’t get that magnetic pole thing out of there though.
And cosmic rays.
But are they unidirectional and do they penetrate the Earth like magnetic flux? No, they aren’t and no they don’t; in that order.
Or are you saying that the cobwebs have company? 
There is an Arabian proverb:
I came here as the second man, in pursuit of the fourth man, that I should not become the first man.
To those of you who have answered my interrogatories, perhaps even as your eyes rolled and you were thinking “Is this guy for real or is he just yankin’ our chain?”, a heartfelt and sincere thank you. You made me feel welcome.
My questions were real, and those “weird” ideas have been rattling around in my cranium unanswered since the first time I ever encountered the scenario of a body falling through the Earth. Now they are answered – because you took the time to do so.
**I now know that gravity is symmetrical;
I know that regardless of the mass that surrounds a body, the effects of gravity are not dependent upon the relationship of the mass to the body but the mass as a whole, i.e.: gravity acts on a body linearly to the center of the mass;
I know that a hollow spherical shell, regardless of the mass contained in the shell, has zero gravity within the void;
I know that even if the spherical body is solid, the spherical shell acts in the same manner as if it were hollow;
The placement of the tunnel through the rotational axis was elementary, but the magnetic axis still throws me.**
Conversely:
For those who have no patience with people such as myself, a gentle reminder:
At some point in your life, you were as ignorant as me.
I learn something new every day.
Welcome to the board.
As for the magnetic effects, it depends on what question is being asked. In physics, one never assumes that one is really talking about all the effects on an object, because that’s completely impossible. Usually, you just consider the most important effect, and maybe some of the less important effects if they’re significant. So when you see a question like “What happens if I fall through a tunnel through the Earth”, your first thought should be gravity, since that’s going to be the dominant effect. Air resistance, friction with the sides, and rotational effects aren’t completely overwhelmed by the gravitational effects, so you might want to consider those, also. But when you get to things as weak as the magnetic field of the Earth acting on a human body, it’s hard to tell where to stop. Do you consider the effect of electrostatic forces from the guy shuffling his feet on the carpet before he fell in? How about the fact that the Earth isn’t perfectly spherically symmetric: That’s going to change the answer slightly. What about when our free-faller is overcome by the urge to spit, when looking down into the deeps… That puts a little extra force on him. Or how about a chance cosmic ray which hits him, and puts a little force on him? The fact is, assuming that you’re falling in vacuum is already a lot bigger assumption than assuming that the magnetic field is irrelevant.
You can, of course, specify in the question “Assuming that magnetic forces and gravity are the only relevant forces, what happens…”, in which case you should consider magnetism. But that’s not really the question, here.
By the way, about magnetism of the human body: Metallic iron is ferromagnetic, but iron compounds aren’t necessesarily, and we don’t have much iron in us, anyway. What’s more relevant is the magnetism of water, since we’ve so much water. Almost all materials are either paramagnetic or diamagnetic; paramagnetic materials are weakly attracted to a magnet (but they don’t “remember” being magnetized, like iron does), while diamagnetic materials like water are weakly repelled by a magnet. These effects are hard to notice with ordinary refrigerator magnets, but with a strong enough magnet you can levitate a frog (or a human, if you had one big enough, but alas, we don’t, yet).
While the excercise started out as the classic “falling through the Earth” scenario, various outside influences were subsequently addressed; air friction and Earth rotation among them.
As I recall, the original premise of the excercise, way back when, was that the subject body would fall through center and would undulate back and forth pendulum-like with a decreasing harmonic due to losses from air until it came to a halt at the exact center of the mass, rather than continuing for eternity.
In the discussion of the eternal aspect of the excercise, the question of operating in a vacuum was address and thrown into the mix.
Another poster addressed the Earth’s rotation and how, if the tunnel were straight, the body would be thrown against the walls of the tunnel. That would certainly increase the friction.
The only way to address the rotation other than making the tunnel a spiral (the return trip would be a b----, though) was to place the tunnel exactly centered on the rotational axis.
The thing that I found unaddressed was what the effect of the Earth’s magnetic field would have on the body. Magnetic Resonance Imaging (MRI) depends on the body’s magnetic aspects and I posted links to explanatory webpages to this effect.
CHAPTER-3 is one of those pages and explains the aspect of “spin” in lay language and how the atomic particles of various Elements within the body react to outside magnetic influences. Even setting aside the influence of iron, there are enough other Elements within the body to cause an effect. I find this to be significant. Not trying to be a hard a-- but I also seem to be the only one who does.
If the subject body, falling down the perfectly axially-aligned tunnel, through a perfect vacuum is operating at zero gravity; and it is being acted upon by nothing more than the gravity pulling it “down”, any other force which may act upon it, in that environment, could have a significant effect.
The only thing left to address, other than the random cosmic particle – which is not unidirectional in nature nor of significant force – hitting the subject body, is the Earth’s magnetic poles. These poles wobble in a randomly oval pattern on a daily basis and are subject to outside magnetic influences such as sunspots which may cause them to wander as much as 80Km. In addition, the position of the area circumscribed by the oval moves ~40Km / yr. So the flux gets stronger and weaker relative to the rotational axis by virtue of this movement.
The significant aspect of the magnetic field is that it is offset from the rotational axis of the Earth and, I believe, that the falling body under the environment described could – note could – be slung against the wall of the tunnel upsetting the entire apple cart. It would not take much force on a body under the environment stated to move that body.
I used to work at a company that manufactured spaceborne data tape recorders. We had to make the reels of the recorder contrarotate because if they both rotated in the same direction it would change the attitude of the spacecraft.
I was in charge of the documentation of the Mass Memory Unit (MMU) and High Data Rate Recorder (HDRR) for the space shuttle and even those units, for a craft that size, were required to have contrarotating reels.
So it doesn’t take a whole lot to move a body in zero gravity in a vacuum.
At the time the “falling through the Earth” excercise was first addressed, there were no MRIs. In fact, I don’t believe that atomic particles had been addressed either. I remember the first time I heard this scenario when I was a kid (about 1962 or so) and it was a very old excercise then.
If you want to watch the effect in operation, you have nothing more to do than go watch your electric meter rotate. The plate that rotates within it is made of aluminum but is moved by magnetic flux.
If you had a magnet powerful enough to levitate a human body, wouldn’t it also be powerful enough to tear the body apart? How would one control the varying lift of arms and legs vs torso? God help 'em if they are wearing a belt buckle.