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Youjaes
USA
28 Posts |
 Posted - 19 Aug 2002 : 23:46:17
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My experience in "The fLaw of Gravity" thread has been going around in my head and I've been getting stuck in a bit of a quandary, that goes as follows:
A uniform spherical shell of uniform mass is encompassed by a larger spherical shell of uniform mass with the centers of the two shells coinciding at the same point.
Now, for each and every unit of mass of the inner spherical shell, there is a net attractive force of zero exerted on it by the outer shell, yet for each and every unit of mass of the outer shell, there is a net attractive force inward that is non-zero. Therein lies my quandary.
We have a radially compressive force on the outer spherical shell towards the inner one, but not an opposite and equal decompressive force on the inner spherical shell towards the outer one. I'm stuck on reconciling this one at the moment....perhaps a night's sleep will clear the fog for me.
James
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AgoraBasta
Russia
234 Posts |
Posted - 20 Aug 2002 : 07:33:34
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quote:
We have a radially compressive force on the outer spherical shell towards the inner one, but not an opposite and equal decompressive force on the inner spherical shell towards the outer one.
And hence the pressure arises. How misterious!
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Jim
1582 Posts |
Posted - 20 Aug 2002 : 11:28:57
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The two mass centers can be at the same point and the two gravity centers not. The mass of a shell is spread out over a surface and so is the gravity force so the pressure and temperature will not be more at the center of mass than it is at the surface and will be greater at the midpoint between the two surfaces.
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tvanflandern
USA
2793 Posts |
Posted - 20 Aug 2002 : 11:40:20
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quote:
We have a radially compressive force on the outer spherical shell towards the inner one, but not an opposite and equal decompressive force on the inner spherical shell towards the outer one.
Newton's third law of motion is greatly over-rated because it doesn't really apply to gravity, even though we compel it to apply by creating unobservable fictions. In the above case, as AB says, the counter-force manifests itself as downward pressure.
But I prefer a different way of understanding all this. Suppose we have a series of masses all at the same distance from the Sun. Let's say these masses are: 1000-solar-mass black hole; Jupiter; comet; dust grain; and a single neutron. Ignoring the effect these masses have or fail to have on the Sun, the Sun causes all of them to accelerate toward itself at exactly the same rate. That is because, as Galileo's Tower of Pisa experiment showed, the rate at which bodies accelerate in a gravitational field is independent of their own mass. Heavy and light bodies fall at the same rate.
If Newton had formulated his law of gravitation in this way, we would have no confusion over this issue. But instead of describing the acceleration of bodies in a gravitational field, which we can observe and verify, Newton wrote his law as a force law, even though we cannot observe forces.
So if you wish to understand physics by explaining that the Sun's force on any of those different target bodies is proportional to the product of the masses of the Sun and target body, but the acceleration of each target body is the same because the "force of inertia" counters the "force of gravity", more power to you. But if you want to achieve a clearer understanding of nature and gravity, I recommend recognizing that the acceleration of gravity is independent of the mass of the target body, and that inertia is not operative at all in the case of gravity. So Newton's third law doesn't hold either.
You can read more about this way of thinking in Pushing Gravity. -|Tom|-
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AgoraBasta
Russia
234 Posts |
Posted - 20 Aug 2002 : 11:50:05
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Or one can consider the local gravity as being rigidly attached to the local aether of density proportional to the gravity, and get an equivalent of GR. Question then would be - how to account for a completely physical pressure?
BTW, Tom, if I kick you (gently), you'll notice that force is more physical than acceleration. Acceleration needs space and time to manifest itself, while force requires neither of those, thus being as basic a category as space/time themselves.
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Jim
1582 Posts |
Posted - 20 Aug 2002 : 11:57:30
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The 1000 solar mass will not move to the 1 solar mass the 1 solar mass will not move to the the .001 solar mass. The reason is what? If not inertia then what do you call the effect that makes the smaller mass move and not the larger mass.
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tvanflandern
USA
2793 Posts |
Posted - 20 Aug 2002 : 12:22:19
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[AB]: BTW, Tom, if I kick you (gently), you'll notice that force is more physical than acceleration.
That is true for electromagnetic and mechanical forces. My point is that gravity is different -- gravity produces inertia-free acceleration.
If I retaliate for the kick by sending my pet 1000-solar-mass "black hole" in your direction, you will never see or feel it coming. Your first clue that you are about to be sucked into oblivion will be a large acceleration relative to distant objects. 
quote:
[Jim]: The 1000 solar mass will not move to the 1 solar mass the 1 solar mass will not move to the the .001 solar mass. The reason is what? If not inertia then what do you call the effect that makes the smaller mass move and not the larger mass.
Bodies of all masses fall toward the Sun at the same rate -- a rate that depends on the Sun's mass. If you wish to look at the reciprocal question of what happens to the Sun (which is irrelevant for purposes of my example), then we could replace the sun with a 1000-solar-mass black hole or a neutron, and the results are the same. Any of the above will accelerate toward the distant bodies at a rate that depends on each distant body's mass, but is independent of the Sun's mass (or the mass of whatever you put there in place of the Sun).
Gravitational acceleration depends on the mass of the gravitating body, but not on the mass of the body being moved. When two bodies are involved, the acceleration each produces in the other depends on its own mass, and not on the other's mass. -|Tom|-
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AgoraBasta
Russia
234 Posts |
Posted - 20 Aug 2002 : 12:31:04
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My point is that gravity is different -- gravity produces inertia-free acceleration.
That's a very big "if", had gravity proved "shieldable".
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If I retaliate for the kick by sending my pet 1000-solar-mass "black hole" in your direction, you will never see or feel it coming. Your first clue that you are about to be sucked into oblivion will be a large acceleration relative to distant objects.
Hadn't those dogs been outlawed at this board?
Also, after the universe, not me, sinks into oblivion, I will get hit by whatsoever is there under horizon. Not fair!
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Jim
1582 Posts |
Posted - 20 Aug 2002 : 12:35:14
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Well for the third or fourth time I aggree with you about acceleration of gravity. The point is the small mass is moved and the large mass is not moved. This result is why the large mass has tides and the small mass has velocity. You can pick on the model here since both masses are effected the same in one sense and differently in another sense.
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tvanflandern
USA
2793 Posts |
Posted - 20 Aug 2002 : 15:56:47
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[Jim]: The point is the small mass is moved and the large mass is not moved.
That statement is in error. The small mass makes the large body move too, in proportion to its own small mass. For example, both Earth and Moon raise tides on one another. Earth makes the Moon move in a large orbit, and the Moon makes the Earth move in a smaller orbit (81 times smaller, because the Moon has 81 times less mass).
So the Earth-Moon barycenter (the point that orbits the Sun in an elliptical orbit) is located about 1000 miles inside the Earth, about 1/4 of the way to the center. And the center of the Earth revolves around the barycenter once each lunar month. -|Tom|-
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AgoraBasta
Russia
234 Posts |
Posted - 20 Aug 2002 : 16:16:17
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Tom,
Is there any consistent data on the Sun's motion wrt the Solar system barycenter? Also, is there any difference in motion of the Sun's geometric centre and its magnetic field centre?
Hardly this question belongs in this thread, but I just have no idea where to stick it.
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tvanflandern
USA
2793 Posts |
Posted - 20 Aug 2002 : 16:29:37
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[AN]:Is there any consistent data on the Sun's motion wrt the Solar system barycenter? Also, is there any difference in motion of the Sun's geometric centre and its magnetic field centre?
The Sun's motion wrt the solar system barycenter is calculated because the barycenter cannot be observed. In fact, its location is a matter of arbitrary definition, and not of physics. For example, if we include Alpha Centauri along with the Sun and its planets in our dynamical system, the barycenter moves half-way to Alpha Centauri without any observable consequences.
I am unaware of any observable distinction between the Sun's geometric center and its magnetic field center. Such a thing might exist, as it does for planets; but I've not heard of it for the Sun. -|Tom|-
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Jim
1582 Posts |
Posted - 20 Aug 2002 : 20:42:24
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The moon then by this logic orbits 81 times faster than the Earth? So the GM=RV2 rule must be false since it indicates the moon orbits 9 times faster. And is the moon tide very much bigger than the tide on Earth?
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Larry Burford
USA
1337 Posts |
Posted - 22 Aug 2002 : 07:41:24
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[ab]
Is there any consistent data on the Sun's motion wrt the Solar system
barycenter? Also, is there any difference in motion of the Sun's geometric centre and its magnetic field centre?
[tvf]
The Sun's motion wrt the solar system barycenter is calculated because the barycenter cannot be observed. In fact, its location is a matter of arbitrary definition, and not of physics. For example, if we include Alpha Centauri along with the Sun and its planets in our dynamical system, the barycenter moves half-way to Alpha Centauri without any observable consequences.
======
This is rather unexpected. I'm intrigued.
Assuming that you are not pulling our leg, WHY would we want to allow for the possiblilty of including Alpha Centauri when determining the barycenter of "the Solar system"? Doesn't your example describe the approximate location of the barycenter of the Solar/Alpha Centauri "system"?
I've never seen a formal definition of barycenter - from context I had always assumed it was the technical term for center of mass. My CRC doesn't mention it and the Internet says "...center of mass...".
The location of a center of mass obviously depends on which masses you are talking about. Specifying "the Solar system" should exclude things like the Centauri triplets or the Sombrero Galaxy.
What am I missing here?
Regards,
LB
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Jim
1582 Posts |
Posted - 22 Aug 2002 : 11:52:07
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The barycenter is a model that balances the two mass centers as one would do on a balance scale. It is in common use today and no one thinks that is wrong because it has been in use for a few centuries. The error with this model is that in a dynamic system the static balance is not stable due to the fact the smaller mass is spinning way to fast to be offset by the slower and larger mass. The model is bogus.
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tvanflandern
USA
2793 Posts |
Posted - 22 Aug 2002 : 23:26:56
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[Jim]: The moon then by this logic orbits 81 times faster than the Earth? So the GM=RV^2 rule must be false since it indicates the moon orbits 9 times faster.
81 times faster is correct. The law you cite refers to the orbit of the Moon relative to the Earth, or to any real circular orbit and its center. It does not apply to motion around fictitious points such as the barycenter. No mass is located at the barycenter.
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:And is the moon tide very much bigger than the tide on Earth?
The Moon tide is nearly 1000 times larger than Earth tides. That is partly because Earth's mass is so much larger than the Moon's, and partly because the Moon does not rotate, so the "tide" (or bulge, if you prefer) is permanent. -|Tom|-
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tvanflandern
USA
2793 Posts |
Posted - 22 Aug 2002 : 23:36:25
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WHY would we want to allow for the possiblilty of including Alpha Centauri when determining the barycenter of "the Solar system"? Doesn't your example describe the approximate location of the barycenter of the Solar/Alpha Centauri "system"?
The example is intended to illustrate how arbitrary "barycenter" is. It applies to all the masses under consideration. That line can be drawn wherever we please.
A "universe" (dynamical system) consisting of Sun, planets, and Alpha Centauri is just as valid as one consisting of Sun and planets only. Barycenter can be equated with "center of mass".
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Specifying "the Solar system" should exclude things like the Centauri triplets or the Sombrero Galaxy.
My point is just as valid if I said "include the mass of hypothetical Planet X with a Jupiter-sized mass orbiting the Sun at a distance of 1000 au". That is certainly a legitimate part of the solar system, yet would drag the barycenter out to the Earth's orbit. The Earth sometimes would go right through it. But nothing we can observe changes. -|Tom|-
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Larry Burford
USA
1337 Posts |
Posted - 23 Aug 2002 : 08:23:44
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[tvf]
The example is intended to illustrate how arbitrary "barycenter" is. It applies to all the masses under consideration. That line can be drawn wherever we please.
A "universe" (dynamical system) consisting of Sun, planets, and Alpha Centauri is just as valid as one consisting of Sun and planets only. Barycenter can be equated with "center of mass".
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I guess I'm not making myself clear. I understand THAT we can include any mass in our definition of a dynamical system. But I'm not sure WHY we would consider adding some masses to some systems.
Rather than try to rephrase my original question, though, let me try a different approach. Just before AB asked his question about the barycenter of the solar system (to which you made your reply referencing Alpha Centauri) you had mentined the barycenter of the Earth-Moon system. When you specified "Earth-Moon" you clearly meant to exclude all other masses. True? In this case there is no ambiguity about the definition of the dynamical system or where the barycenter of that system is located. True?
AB specified the Solar system in his question. No specific masses were explicitly mentioned, so the definition of the dynamical system is ambiguous, and open to modification. True?
(Damn! You have been Tholenized! Seriously though, it is important to be precise. Ambiguity leads to many misunderstandings and disagreements.)
AB's question was: "Is there any consistent data on the Sun's motion wrt the Solar system barycenter?" If this question were to be reworded thus: "Is there any consistent data on the Sun's motion wrt the Sol-Jupiter (or Sol-Jupiter-Saturn, etc.) system barycenter?", I'm guessing the ambiguity would go away. True?
On the topic of calculating vs observing the barycenter of a system. Aren't we observing the barycenter of a star system (the star and whatever mass is within its gravitational sphere of influence) when we use the star's wobble to detect things orbiting it?
We can also look at Sol and see it wobble. But in this case we can identify just about all of the mass causing that wobble.
Is there a different term for the center point of this wobble? Perhaps "wobblecenter"? Since this is an observable point in space, it would seem not to be the same in general as barycenter. Of course if you pick your dynamical system carefully it could be the same point.
Regards,
LB
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AgoraBasta
Russia
234 Posts |
Posted - 23 Aug 2002 : 09:11:01
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So now my question would be - is the Sun wobbling consistently with the known composition of the Solar system? And how is the observed "visible" Sun, after the corrections to light transit times are made, placed wrt its magnetic field and its gravitational field?
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tvanflandern
USA
2793 Posts |
Posted - 23 Aug 2002 : 12:44:03
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[LB]: I'm not sure WHY we would consider adding some masses to some systems.
I was illustrating arbitrariness and lack of physical significance for the point called “barycenter”. All real systems have slightly uncertain masses and the possibility of other, unknown masses. These change the barycenter, but not the physics.
I have some correspondents who attach physical significance to “barycenter”, and who derive things such as the centrifugal forces on various points on Earth’s surface due to their differing motions with respect to the Earth-Moon barycenter. This is physical nonsense. The motion of Earth with respect to the Earth-Moon barycenter has no more physical significance than its motion with respect to any other arbitrary point in space, such as the point midway between Earth and Moon.
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When you specified "Earth-Moon" you clearly meant to exclude all other masses. True? In this case there is no ambiguity about the definition of the dynamical system or where the barycenter of that system is located. True?
True. To the extent that “barycenter” is a computed point, its location is never ambiguous. The ambiguity arises from not knowing any masses exactly or completely, or where to draw the line about what to include.
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If this question were to be reworded thus: "Is there any consistent data on the Sun's motion wrt the Sol-Jupiter (or Sol-Jupiter-Saturn, etc.) system barycenter?", I'm guessing the ambiguity would go away. True?
There cannot be “data” about a barycenter for any system of masses because a barycenter is not a physical, observable point. It is a purely mathematical one. If you specify the masses, then the computation should be exact. But so what?
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On the topic of calculating vs observing the barycenter of a system. Aren't we observing the barycenter of a star system (the star and whatever mass is within its gravitational sphere of influence) when we use the star's wobble to detect things orbiting it?
No, we are just observing the relative motion of two bodies, as we always are. Once we have enough data to estimate the separate masses, we become able to compute an estimated barycenter location. But we have no way to observe that location. And if we later discover another planet or a distant dwarf star in the same system, so that the barycenter jumps, that does not invalidate our previous work.
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Is there a different term for the center point of this wobble?
No, same term.
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Since this is an observable point in space, it would seem not to be the same in general as barycenter.
It is not observable. It is inferable. We observe the relative motion between bodies. As we do so, we may learn of a short-period orbiter soon. As time goes on, we may learn of more and more orbiting bodies contributing to the wobble.
In my “Planet X” example, the Sun and all known planets may have a huge-but-very-slow wobble with amplitude of 1 au. But there would be almost no relative wobble, so we would remain unaware of the existence of a large, undiscovered mass in our own solar system. -|Tom|-
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tvanflandern
USA
2793 Posts |
Posted - 23 Aug 2002 : 12:50:47
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[AB]: is the Sun wobbling consistently with the known composition of the Solar system?
By definition, yes. If the Sun had some unexplained wobble, that would lead us to infer additional mass in the system. The most accurate data measuring this “wobble” is pulsar timing data. If the Sun moves in some direction, pulses in that direction arrive earlier than expected, and pulses from the opposite direction arrive later than expected.
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And how is the observed "visible" Sun, after the corrections light transit times are made, placed wrt its magnetic field and its gravitational field?
The Sun’s magnetic field is far too weak to detect from Earth. Inferences about it are made based on splitting of certain spectral lines.
The visible and gravitational Sun differ because of the light transit time, and nothing else. That merely means that any undiscovered mass is distant enough to affect Sun and Earth only very slowly and almost identically. -|Tom|-
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My dilemma
