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Settle an argument
Thomas Harte
Member #33
April 2000
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No, because you'd share in the orbital motion around the common center

Good point! I'd made the error you probably think I did, i.e. switched inertial frames for forces but not carried velocity along with me.

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But in the center, those would cancel out, and if it didn't, then the entire orbit would be affected.

Right, but the entire orbit does change over time. I'm sure I read earlier, though I can't find it now, that the position of the Earth now and the position of the Earth exactly a year ago vary by as much as 10,500km (though I can't find the source again, so that figure may be wrong). I'm not saying the differences don't cancel themselves out in the overview, merely that nobody has made a sufficient argument to establish that they have close-to-zero effect on the scale of a person over a very short amount of time.

EDIT:

SiegeLord said:

I won't of course, because it is apparent to me that it is negligible, any of those effects you call attention to would apply equally (or even in greater magnitudes) at the surface of the Earth where each one of us is sitting.

Gosh, I wish you were listening.

(1) will an object that is non-negligibly affected by the gravitation pull of the Earth act in exactly the same way as one that is not affected by the pull of the Earth?

(2) therefore, is it valid to say that if you can observe no effect in objects that are affected by the gravitational pull of the Earth, that you would not be able to observe an effect were that pull removed?

By your token, I can argue that the tiny thrusters astronauts use to manoeuvre themselves when in orbit obviously have negligible effect on them because if I apply the same force to an object sitting next to me in the room then it doesn't move.

Whether or not my argument is false, making arguments that just ignore what we're talking about (ie, that something can't affect an object that is otherwise free of the pull of the Earth because it doesn't affect things that aren't free of the pull) isn't persuasive.

Arthur Kalliokoski
Second in Command
February 2005
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The OP said that "at the Earth's center of gravity the Earth's gravity would have no net effect on an object." If you're at the center of gravity, even momentarily, then you're equally surrounded by mass. And I believe the whole point was that your "weight" would diminish when approaching the center of the earth instead of increasing or remaining constant.

“Throughout history, poverty is the normal condition of man. Advances which permit this norm to be exceeded — here and there, now and then — are the work of an extremely small minority, frequently despised, often condemned, and almost always opposed by all right-thinking people. Whenever this tiny minority is kept from creating, or (as sometimes happens) is driven out of a society, the people then slip back into abject poverty. This is known as "bad luck.”

― Robert A. Heinlein

Thomas Harte
Member #33
April 2000
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The OP said that "at the Earth's center of gravity the Earth's gravity would have no net effect on an object."

He also said "The question in debate is whether or not it was scientifically accepted to say that there would be gravity at the center of the Earth", which brings in questions of whether sources other than the Earth could produce a [non-negligible] gravitational pull at the centre of the Earth.

People then made a whole bunch of statements assuming the centre of mass of the Earth to be a constant position, which is what I consider questionable.

EDIT: in fact, the Earth's centre of mass definitely does move relative to the Earth itself (source), so the question is whether this is non-negligible over a short space of time.

EDIT2: actually, that's a fantastic resource to make my point. I'll quote it in its entirety with emphasis added:

Quote:

It has been found that the residual (Chandler) motion of the Earth's rotation pole results from the forced translational motion of the Earth's rotation axis relative to the geographic axis. The Earth's rotation axis moves parallel to itself without changing the angle of inclination to the ecliptic plane. The translational motion of the Earth's axis of rotation is caused by the motion of the Earth's center of mass in the Earth's body in the range from 1 to 30 meters relative to the Earth's surface. The motion of the Earth's center of mass in space is due to the motion of the consistent inner core of the Earth in the liquid outer core under the action of the total (internal and external) gravitational field. Formulae for calculation of the trajectory of the Earth's centre of mass from astronomical observations are suggested. The comparison of our calculations and observational data on variations in the latitudes of places and acceleration of gravity has shown that they are in good agreement. Our model has been shown to adequately describe the physical process of motion of the Earth's centre of mass inside the Earth's body.

Though it doesn't give an idea of how much time the up-to-30m shift in the centre of gravity (ie, much bigger than a person) takes. If it's 1,000,000 years or whatever then clearly it isn't relevant.

SiegeLord
Member #7,827
October 2006
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ie, that something can't affect an object that is otherwise free of the pull of the Earth because it doesn't affect things that aren't free of the pull

This has nothing to do with making measurements with the pull of the Earth present or not! 34 micrometers per second squared is negligible both with a background 9.8 m/s^2 and with a background 0 m/s^2! I never said there is no effect whatsoever, and I never claimed that this effect is negligible because of the background 'noise'. The effect is negligible because it is negligible, it is tiny! It'd be negligible even on the surface of the sun, or next to the black hole. For humans, such low acceleration cannot be perceived, no matter what other forces affect them.

EDIT: This, at first reading, suggests that the threshold for human perception of acceleration is on the order of several millimeters per second. Over 100x larger than the effects we are dealing with here.

Though it doesn't give an idea of how much time the up-to-30m shift in the centre of gravity (ie, much bigger than a person) takes.

Who cares, when you are 30 meters away from the center of the Earth, you still feel basically no gravity! If you carved out a 30 meter hole at the center, that whole hole would be in a microgravity environment. If you didn't carve out 30 meters, but left a sphere within that hole, that 30 meter radius sphere would not appreciably attract you (the acceleration due to gravity would be around 1*10^-4 m/s^2). If that bothers you, just carve out the final 30 meters. I'm sure the story referenced in the OP did not involve the protagonist trapped in a man sized coffin in the middle of the Earth.

The whole point of the derivation I linked to earlier was that once you have a shell of matter around you, it doesn't matter where in the shell you are, as long as you are inside it.

"For in much wisdom is much grief: and he that increases knowledge increases sorrow."-Ecclesiastes 1:18
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Thomas Harte
Member #33
April 2000
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SiegeLord said:

This has nothing to do with making measurements with the pull of the Earth present or not!

SiegeLord said:

I can integrate over that plot gnolam posted ... and also arrive at some negligible answer. I won't of course, because it is apparent to me that ... any of those effects you call attention to would apply equally (or even in greater magnitudes) at the surface of the Earth

In your opinion, effects apply equally to something subject to the pull of the Earth (eg, something at the surface of the Earth) and to something not subject to the pull of the Earth (eg, something at the centre of mass) but your argument has nothing to do with "making measurements with the pull of the Earth present or not"?

SiegeLord said:

Who cares, when you are 30 meters away from the center of the Earth, you still feel basically no gravity! If you carved out a 30 meter hole at the center, that whole hole would be in a microgravity environment.

Possibly we're just talking at different levels of conceit? If you instantaneously released a body into a 30 metre hole at the centre of mass of the Earth then that body would move relative to its surroundings by the up-to-30 metres, because the inner core would move.

I can see your argument as working only if we pretend that the Earth is a rigid body.

weapon_S
Member #7,859
October 2006
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SiegeLord
Member #7,827
October 2006
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In your opinion, effects apply equally to something subject to the pull of the Earth (eg, something at the surface of the Earth) and to something not subject to the pull of the Earth (eg, something at the centre of mass) but your argument has nothing to do with "making measurements with the pull of the Earth present or not"?

Well, it's not an opinion. Linear superposition of forces is a pretty well accepted property of the universe (it's Newton's Second Law). The moon will pull at me the same amount no matter if the Earth is replaced by a black hole, or by Dustin in his subterranean probe. The law of universal gravitation only depends on the two masses involved, the person, and the body in question (the moon). So yes, it does not matter if the Earth is present or not... it's not in the equation, so the pull of the Earth has no effect.

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Possibly we're just talking at different levels of conceit? If you instantaneously released a body into a 30 metre hole at the centre of mass of the Earth then that body would move relative to its surroundings by the up-to-30 metres, because the inner core would move.

Sure. Movement != perception of the force. You'd observe the Earth moving around you, but if you are just floating, far enough from the wall and closed your eyes (thus relying only on your vestibular sense) you would not be able to tell that the Earth's core is dancing around.

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I can see your argument as working only if we pretend that the Earth is a rigid body.

It has to be rigid to some degree (otherwise the cavern in the centre would collapse on you). Assuming that wall exists, I don't care if the Earth was made entirely from water past that point, the law of gravitation will still apply identically.

"For in much wisdom is much grief: and he that increases knowledge increases sorrow."-Ecclesiastes 1:18
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Thomas Harte
Member #33
April 2000
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SiegeLord said:

Well, it's not an opinion.

You're either being deliberately obtuse or genuinely misunderstanding what I'm saying. Given that you falsely accused me of having a "centre of mass=point source" outlook even though I'd already said "at best you mean that the original equation applies only where gravity is modelled as emanating from a point mass?", it's probably the latter.

You have argued that some forces cannot be significant on a body that is not affected by the gravitational pull of the Earth because they are not significant on bodies that are affected by the gravitational pull of the Earth. When challenged, your response is "This has nothing to do with making measurements with the pull of the Earth present or no".

Your logic doesn't work. It's like saying that a hairdryer can't exert a significant force on a bit of paper because when you used one on a piece of paper under a paperweight, it didn't blow away. Then, when challenged, you respond that the presence or absence of the paperweight has nothing to do with what you're saying.

The exchange, in full:

SiegeLord said:

it is apparent to me that it is negligible, any of those effects you call attention to would apply equally (or even in greater magnitudes) at the surface of the Earth where each one of us is sitting.

making arguments that just ignore what we're talking about (ie, that something can't affect an object that is otherwise free of the pull of the Earth because it doesn't affect things that aren't free of the pull) isn't persuasive.

SiegeLord said:

This has nothing to do with making measurements with the pull of the Earth present or not!

Samuel Henderson
Member #3,757
August 2003
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Quote:
weapon_S said:

Settle an argument

Well, since it seems like people here can't agree that it is even possible for someone to be at the centre of the earth and have absolutely no gravitational forces acting on them I would say that poor Neil is going to have look elsewhere, or at least be willing to accept that the answer presented here is probably divided as well.

My two cents...

Newton came up with his theory and equations and stuff in 1687 (as mentioned) so I assume that at the time (1864) if anyone thought about it they would have used the equations and figured that gravity does not apply at the centre of the earth.

OnlineCop said:

You don't get the "bends" from surfacing too quickly. You get them because your body is getting compressed back to its previous height!

Being a diver I laughed at this :)

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SiegeLord
Member #7,827
October 2006
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Your logic doesn't work. It's like saying that a hairdryer can't exert a significant force on a bit of paper because when you used one on a piece of paper under a paperweight, it didn't blow away. Then, when challenged, you respond that the presence or absence of the paperweight has nothing to do with what you're saying.

That because is of your manufacture. I brought up the example of being on the surface of the Earth because, as I said, we are sitting on it. It has nothing to do with the Earth pulling on you, I made the example so you yourself can easily verify the verity of my statements without digging down to the center of the Earth. The difference I am highlighting between the two locations is not the force of gravity exerted by the Earth, I am highlighting solely the difference of location, and the corresponding lack of difference coming from the effects of the Moon, the Sun and the imperfections of the structure of the Earth.

I am saying that if you don't feel those effects here, you definitely won't feel them 6000 km away from this location at the center of the Earth. 6000 km is nothing compared to the distance of the Moon from the Earth, and even smaller nothing compared to the distance between the Earth and the Sun. Those effects start negligible, and remain so.

The effects of the imperfections of the Earth are greater, because I feel like those imperfections would probably cancel themselves out in the center of the planet relative to their summed effect on its surface. Even if they don't, they are negligible to begin with, as gnolam's diagram shows.

"For in much wisdom is much grief: and he that increases knowledge increases sorrow."-Ecclesiastes 1:18
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Thomas Harte
Member #33
April 2000
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SiegeLord said:

I am saying that if you don't feel those effects here, you definitely won't feel them 6000 km away from this location at the center of the Earth.

And you don't see any potential flaw in "if you're not conscious of something small while also under the influence of something big, then you definitely won't be conscious of it if I take the big thing away"?

If I take your question at face value then, yes, the effect of the Moon's gravity is observable here on the surface, especially to those that live near the coast. And, yes, I think that effect would be more pronounced if I were surrounded by a huge mass of fluid that wasn't as affected by the Earth's pull, internal to the heavy stuff.

I think that clearly states my opinion. Of course I'll continue to defend myself if anyone accuses me of being definitely wrong because I've applied an obviously false model, but otherwise I guess that's all I really need to say to complete my participation in this topic.

GullRaDriel
Member #3,861
September 2003
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OnlineCop owned you :-)

I lawled like a mad cow, man !

_

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Allegro Wiki, full of examples and articles !!

SiegeLord
Member #7,827
October 2006
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And you don't see any potential flaw in "if you're not conscious of something small while also under the influence of something big, then you definitely won't be conscious of it if I take the big thing away"?

The moon can pull me in the direction orthogonal to the direction the Earth pulls me, if the moon is near the horizon. In that perspective, I already can't feel the gravity of the Earth. Not that it matters, I already told you the magnitude of the acceleration due to the Moon, and I already told you the limits of human perception of acceleration. The former is far below the latter.

As for the tides... you are cheating by using a rather sensitive detector of gravity, far more sensitive than a human is. I don't contest that given a sufficiently accurate gravimeter, you'd be able to measure the pull of the Moon, Sun, the Andromeda Galaxy, and any insect that happens to fly around around your cavern. A human would be unable to detect any of those.

"For in much wisdom is much grief: and he that increases knowledge increases sorrow."-Ecclesiastes 1:18
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Matthew Leverton
Supreme Loser
January 1999
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Here's what I've learned so far: If you need an argument settled, don't ask on a.cc!

anonymous
Member #8025
November 2006

Isn't there like two questions here: if you are at rest at the centre of the Earth, how fast will you accelerate towards the centre? How would it feel down there (same as in outer space?)?

alethiophile
Member #9,349
December 2007
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A.cc: where at least the flamewars are about intellectual topics. :P

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OnlineCop
Member #7,919
October 2006
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anonymous said:

How would it feel down there (same as in outer space?)?

You'll start to rotate (gyrate) because of both the magnetic poles of the earth, and because of the rotation of the system. Since the earth, as mentioned earlier, is not uniformly distributed, you will have varying amounts of gravitation pull depending on the land (and water) mass above you.

anonymous said:

if you are at rest at the centre of the Earth, how fast will you accelerate towards the centre?

About as fast as someone on A.cc can get a date with an actual woman. It approaches infinity.

I made a VR game!

Neil Black
Member #7,867
October 2006
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Here's what I've learned so far: If you need an argument settled, don't ask on a.cc!

Yes, that's the main thing I've learned, too. >:(

In response to Thomas Harte:

"I've decided what conclusion I want to reach"

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"We've decided that everybody else must agree with us"

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"We can't see how, were one large body having no gravitational effect on us, any other body could either"

I wasn't aware that the idea that an object would have no net gravitational effect upon another object at it's gravitational center was under contention. Apparently I was wrong, and you disagree.

As for the last quote, I should have said, "The question in debate is whether or not it was scientifically accepted to say that there would be gravity at the center of the Earth from the Earth at the time that Jules Verne wrote "Journey to the Centre of the Earth"." Obviously the moon, the sun, and basically every mass that isn't Earth would still be effecting us. But the effect would be negligible.

Wait, it is true that all objects with mass effect all other objects with mass gravitationally, right? Proportionally to their masses and inversely proportional to the distance between them, right? Or is that under contention as well?

Tobias Dammers
Member #2,604
August 2002
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In an idealized situation, you are a point, and the Earth is a perfect sphere. The net gravity is zero. If your ideal self is not point-shaped, then each part of it that is not at the center would experience a very light force towards the center, but far too small for you to notice.
In the real world, you'd burn or melt long before you reach the center.

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Neil Black
Member #7,867
October 2006
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If your ideal self is not point-shaped, then each part of it that is not at the center would experience a very light force towards the center, but far too small for you to notice.

While my ideal self is not point-shaped, my real self seems to be getting more point-shaped, if you consider round to be point-shaped.

Anyway, the argument is settled for my purposes. Clearly we knew in 1864 that the Earth would exert effectively no net gravity on a person at its center of gravity. I win. 8-)

Tobias Dammers
Member #2,604
August 2002
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my real self seems to be getting more point-shaped, if you consider round to be point-shaped.

No, point-shaped means having zero size in any spatial direction (and thus also zero volume and surface area). You are probably rather growing away from point-shapedness and approaching the Earth's shape (but let's hope you won't reach its actual size).

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"We need Tobias and his awesome trombone, too." - Johan Halmén

Neil Black
Member #7,867
October 2006
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You are probably rather growing away from point-shapedness and approaching the Earth's shape (but let's hope you won't reach its actual size).

Actually now that I think about it I've been getting less Earth-shaped over the last month or so. Probably because I have to walk up The Hill at least twice a day to go to class. I do nearly a mile of walking daily, almost half of it uphill! And conversely, almost half of it is downhill, too. Then there's the level bits. I love the level bits.

Tobias Dammers
Member #2,604
August 2002
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Then there's the level bits. I love the level bits.

I hate the level bits. Especially when it comes to making games. As soon as the game is ready to add levels and other content, I lose interest and drop the project.

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Me make music: Triofobie
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"We need Tobias and his awesome trombone, too." - Johan Halmén

Evert
Member #794
November 2000
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Hmm... I'm late to the party and I didn't read every post. Presumably the answer has been given, but I'll just add in case no one mentioned this.

The question in debate is whether or not it was scientifically accepted to say that there would be gravity at the center of the Earth at the time that Jules Verne wrote "Journey to the Centre of the Earth".

Was it a scientifically valid theory (or hypothesis) to say that there would be gravity, in the sense of being able to walk around normally, in 1864?

There is no net gravitational acceleration at the centre of an isotropic mass distribution. The proof for this is quite simple and was given by Newton in the Principia in 1687.
Note that this does notsay that there is no gravity, just that the net acceleration due to gravity is zero.

This proof needs two assumptions: there is no other source of gravity (fairly good approximation on Earth; the Earth is very clearly the dominant source of gravity near here. Tides are irrelevant to this) and the mass distribution is spherically symmetric (ie, radial shells have a uniform density). This is also a fairly good approximation. True, the Earth is neither smooth nor spherical, but the deviations are small.

So no, there was no reason to say that there was gravity at the centre of the Earth in 1864. It's been a long time since I read Journey to the centre of the Earth, but as far as I recall, Jules Verne says as much at one point and makes no claim to the contrary. Note that the journey described in the book comes no where close to the centre of the Earth anyway.

Wait, it is true that all objects with mass effect all other objects with mass gravitationally, right?

Yes. Actually, all objects that have energy (which is all of them), since gravity acts on energy rather than mass.

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Proportionally to their masses and inversely proportional to the distance between them, right?

Mmmmmmmmmmsortofmostofthetimebutnotreally. See below.

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Or is that under contention as well?

Not at all. Gravity in general is described by Einstein's theory of general relativity, which is not F=GMm/r2 er but something more complicated. However, in the low energy/low velocity limit, it reduces to Newtonian gravity.

Arthur Kalliokoski
Second in Command
February 2005
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I always wondered about the Leaning Tower of Piza, the plumb bobs and spirit levels were thrown off when the earth's center of gravity, the moon, and planetary alignment all conspired together

“Throughout history, poverty is the normal condition of man. Advances which permit this norm to be exceeded — here and there, now and then — are the work of an extremely small minority, frequently despised, often condemned, and almost always opposed by all right-thinking people. Whenever this tiny minority is kept from creating, or (as sometimes happens) is driven out of a society, the people then slip back into abject poverty. This is known as "bad luck.”

― Robert A. Heinlein

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