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Gravitational pull at the center of the Earth

  1. Jun 28, 2009 #1
    First, I'm not a physicist. But I do think of the subject often. A simple observation, as you move away from Earth the gravitational pull decreases. OK let's say we can drill a hole through the center of the earth what is the gravitational pull as we reach the middle? Is your answer fact, theory, or accepted theory. I add this part, because I grow tired of answers being set forth as fact and not accepted theory. Therefore if it is fact, has it been proven? That is, given that we have drilled a few holes in the Earth more than a mile or so. And I admit I being somewhat silly here, has anyone drop something in it that proves what you are saying.
  2. jcsd
  3. Jun 28, 2009 #2
    you drill a hole ,and drop it, you will know if its fact or theory
  4. Jun 28, 2009 #3


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    Fact, theory, accepted theory..Oh my :eek:

    http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm (Towards the bottom. Field Inside a Spherical Shell)
  5. Jun 28, 2009 #4

    Great web reference. Monty37 not so great reply. But no one has answered the proof part of my question. Has anyone proven that the formula mentioned are correct for inside a sphere. Yes the formula are well proven for outside and on the surface of a sphere. But we are talking INSIDE. So has anyone demonstrated that gravity in affect decreases as you approach the center due to the opposing forces of mass.
  6. Jun 28, 2009 #5
    No, nobody has even drilled a hole to the center of the earth.

    If you mean in a small sphere here on the center of the earth, maybe, but the gravitational force of that small sphere is so tiny that it is most probably not measurable.

    On the other hand, if you got an insulating charged sphere, you will see that the electric field in that sphere shows the exact same behavior. I think it's safe to say that anyone has tested that experimentally, although I've never heard of it...

    I must say, if you don't believe the spherical shell theorem then you must be very skeptical... It follows logically that you think gravity as Newton explained it is completely false (not only a tiny bit false, as it is, but completely). I very much doubt that you actually think that, so why do you want experimental proof of this?
  7. Jun 28, 2009 #6


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    Here's a similar question:
    How much will a 10kg sack of potatoes weigh on the Moon?

    No one has ever brought a sack of potatoes to the Moon, let alone weighed it there.
    However, I can say with confidence that the answer will be 16.3N.

    Is that answer based on fact or on theory?

    We have not actualy drilled a hole to the centre of the Earth and dropped a rock down there, but the physics is well understood.

    The problem you are encountering in my opinion is that it is the type of question that laypeople think they can answer intuitively - except that the answer is non-intuitive. It merely requires a better understanding of the physics than most laypeople have.
  8. Jun 28, 2009 #7
    Nick89, good answer. DaveC42.. not so good. There is nothing wrong in asking for proof. A simple example, when Neal Armstrong walked on the moon he dropped a feather and a hammer they both fell at the same rate as was predicted, but my point is up to that point in time no one had actually PROVED the formula in a simple/straightforward way.

    Nick it's not that I don't believe in the theorem. But you said it yourself it is a THEOREM, not fact. So does anyone know if someone has done a "Neal Armstrong" here on this theorem.

    Because I'm about to take this 'conversation' to a whole new level.
  9. Jun 28, 2009 #8
    It is fact actually. The shell theorem is derived using only Newton's laws for gravitation. If the shell theorem is false, either Newton was completely wrong, or maths is completely wrong. Due to the fact that Newton's theory of gravitation works extremely well (at low speeds), in other, tested, cases, we can establish that the shell theorem must be true. If it's not true, Newton's laws would not be true, and we could not have experimentally tested any other law that relies on Newton's laws.
  10. Jun 28, 2009 #9


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    But that does not make it fact.
  11. Jun 28, 2009 #10


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    But he did not drop a sack of potatoes. We extrapolate based on known physics. Of course, I am using a silly example.

    Nevermind. I see your point. You want to see experimental evidence of the general formula; it doesn't have to be a specific case of 'all the way to the centre of the Earth'.
    Last edited: Jun 28, 2009
  12. Jun 28, 2009 #11
    That's right DaveC... Since we have drilled a few holes more than a mile deep. I'm thinking (definitely simplistically) if we dropped some instrument down the hole would it prove this theorem. Or as Nick mentioned have what we have drilled not deep enough to 'prove' this.

    You guys ready to take this to the next level. Because this is the question I raised to myself that took me here to begin with. What formed the planet. I have read bits and pieces on this subject and bottom-line there are definitely a couple of theories, but they both revolve around gravity, and yet both theories admit that gravity unlikely does not have the force to cause the 'clumping' to ultimately form a planet.

    So I postulate this idea. What if it is the equivalent of a micro black hole that caused the coalescent of matter to form a planet. The hole large enough to coalesce matter but not so great to collapse it into a greater black hole. Or if you prefer some other entity (worm hole) for example, ie don't get wrapped up on black holes (I'm using that as just one possibility) but some other force at play, be it black, worm, or string. This idea could be elevated if we saw gravity actually increased as we approached the center of the earth and not decreased. Because I do believe in Newton laws as they relate to spherical objects, I just question as to if there is something else at play as it relates to a planet. Therefore the need of fact vs theory.
  13. Jun 28, 2009 #12


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    Last edited by a moderator: Apr 24, 2017
  14. Jun 28, 2009 #13
    I'm not sure what you mean. Are you saying I should have started this thread elsewhere?
  15. Jun 28, 2009 #14
    Observations must be interpreted using some theory anyway. If you were to do an experiment by drilling a hole of some length into the Earth and measure the strength of gravity as a function of depth, then the results will also depend on the theory that explains how your measurement apparatus works.

    In the hypothetical case where gravity works differently so that it is not proportial to M(R)/R^2, most of the physics literature would be flawed which would mean that the scientific measurement devices cannot be trusted. This then means that while you could verify that gravity and the measurement apparatus works according to theory, you cannot really quantitatively detect a large violation of the M(R)/R^2 formula as in that case your measurement device would most likely be flawed as well.
  16. Jun 28, 2009 #15

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    In the sense you are asking for, yes there is. There are in fact many things wrong with what you are asking for.

    First off, you are asking for an experiment that in all likelihood can never be performed. Sans a force field that rivals the imagination of science fiction writers, there is no way to send a probe to the center of the Earth. Rejecting the premise that the weight is zero at the center of the Earth implicitly makes an argumentum ad ignorantiam, an appeal to ignorance: That a premise is false because it has not been proven true.

    There is no such thing as proof in science. Scientific theories cannot be proven to be true. They can only be proven to be false. Dave C's example was a good one. We do not know, with absolute certainty, how much a 10kg sack of potatoes will weigh on the Moon until someone has done the experiment. Even then, we won't know with absolute certainty whether that sack will have a different weight the next time someone does the experiment.

    Science, like the law, does not work on the basis of absolute certainty. Both science and the law work on the basis of reasonable doubt. With this metric, there is no doubt, within reason, what that sack of potatoes will weigh on the Moon (or atop Mt. Everest) without even doing the experiment. The physics and the mathematics are very well understood and there is no reason to think otherwise.

    The same goes for the weight of something at the center of the Earth. Assuming that our models of how gravity works are correct, the mathematics (and the underlying math can be proven) says that the weight at the center of the Earth will be zero. One of these assumptions is that the gravitational attraction toward some object is the cumulative gravitational attraction toward the elementary particles that comprise the object. To say that the gravitational attraction at the center of the Earth is non-zero contradicts this basic assumption.

    The gravitational attraction at the surface of the Earth is directed inward everywhere on the surface of the Earth. If gravitational attraction is a continuous function, then mathematically there must exist a point somewhere inside the surface at which the gravitational attraction is zero.

    Finally, gravity is similar in form to electrostatic force. Gauss' law for gravity and Gauss' law for electrical flux are very similar in form. The latter says that the electric flux through any closed surface is proportional to the enclosed electric charge while the former says the gravitational flux through any closed surface is proportional to the enclosed mass. Gauss' law for electrical flux has been demonstrated and is the underlying reason why you are told to get inside your car in a lightning storm.

    You need to read up on the difference between theorems and theories.
  17. Jun 28, 2009 #16

    The points you make are quite true and I might add very well thought out. In particular, the one that in most case you can not prove an idea to be true, but rather only prove that it is not. And this is exactly what I'm asking. Has an experiment been performed using the earth as the sphere that shows the idea not to be true. Of course, ideally, it would prove the idea to be true. And I'm not so naive to think we can drill hole to the center of the Earth. Shoot we can barely scratch the mantle's surface. But perhaps a 2 or 3 mile hole might be enough I simply don't know. The math works for sphere, I'm asking does it work for the sub-surface of the Earth or indeed is the possibility of other forces might also be at work?

    And I believe the laws of gravity to be accurate, but if a test was performed sub-surface only to discover that there 'seem to be an issue' then that would open the discussion to 'Well what else is going on down there'.

    I might add that Einstein and Tesla both asked themselves why before delving into the math. In both cases believing that the math at the time seem to be true at the time found instances that it was not. They used simple observation of nature as the analogy to formulate their famous theories.

    Bottom-line and thinking outside the box. If gravity can not explain why the planet formed is there another force that either acting as the seed to planet formation (with gravity eventually taking over) once enough mass was accumulated or perhaps this force is still there. I asked the gravity question as one avenue to my thinking outside the box. I would love to hear your 'speculation' on how a planet formed if gravity is not the force that initialized the process.
  18. Jun 28, 2009 #17
    Ok, let's say we DID dig a hole, 2 or 3 miles deep, and verified that the gravitational force is indeed proportional to the radius (and hence, zero at the center). Do you then believe the force is zero at the center? Why would that be any different to what you know now??
    Heck, we may have even done that experiment before!

    And no, no experiment has been performed that proved the shell theorem wrong. If it were, it would probably be headline news, even in the 'normal newspapers', since that would mean the very foundation of nearly all our understanding of gravity are WRONG.

    I think I know what you're getting at here... You mean that people in the past have been 'blinded' by what other people had told them was true, like how the earth was the center of the universe for example. I agree, there were loads of people who simply did not even want to try to disprove that idea, it simply had to be true, because it had always been that way.

    The differences with those people, is that they did not have any firm foundation on which their claims were built. The fact that the earth was supposed to be in the center of the universe was pulled from thin air, just because it is what god had intended.

    Our theories of gravity on the other hand, have a firm basis, in maths, and other physics. They are not pulled out of thin air, and they are tested in many many many other cases. Just that we did not test this one tiny detail, does not mean we are ignorant and are simply assuming that it is true.

    As others put it, we KNOW, within a certain range, the weight of a cow on the moon, even though we have never actually brought a cow to the moon to verify it.
  19. Jun 28, 2009 #18


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    If it wasn't zero, which direction would it point to, and why?
  20. Jun 28, 2009 #19

    It will point in the direction away from the tunnel that connects the hole to the surface.
  21. Jun 28, 2009 #20


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    Eerh, actually this proof is illustrated in basically every high school physics class. I believe it's a two or three liner.

    Where did you get the idea that gravity is not responsible for planet formation??? I see no mention of that in this thread, other than you saying it is so and citing no references.

    While it is true that planet formation is not a completely well understood phenomenon, our present theories are the best we have.

    Look, any amount of science rests on underlying assumptions. From these assumptions we derive things, and if these things turn out to accurately represent the real world, then the assumptions are strengthened. Asking for proof is okay up to a point, but we cannot individually prove every single special case. After all, that's why we have LAWS, and not a book of statements: #1932432: In Geneva, Switzerland, a hammer dropped from the hand of a man 6'3" tall will fall at a rate of 9.8m/s^2, #1932433:....
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