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Author
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Topic: Gravity: mass and the center of mass
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Danpech
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Member # 163
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posted 18. September 2002 09:11
Gravitational physics might seem an unfitting topic for Brainstorms, and, despite having obtained the welcome of ISCID to post on just such a topic, per qualification as a complex system, I don't feel sure that gravitational physics really qualifies. But, then, I'm not so clear on what complex systems is so as to include this subject. Perhaps someone can explain here how it is.
Anyway, on to the subject, and my proposal:
The force of attraction between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The above formula I agree with.
But, people who I suppose are qualified to tell me about the geometric logic of Newtonian gravity have said that the center point of a mass is the point of origin of the gravity of the mass, so that the smaller is a mass, the stronger the gravity per unit mass when standing on the surface of the body [ see http://brp.arc.nasa.gov/Science/Y_GBL/bsc_resrch.html fourth question down ]. I don't see how this can be logically deduced from the above formula, and so I take it to be incorrect. It seems to me to be saying not only that a mass has some odd power to transfer its gravity to a single
point at its center, but that the closer to the center of mass is a point, the greater the pressure per unit mass is on that point.
But, before we can answer whether the center of a mass produces the gravity of the mass, we must answer the problem of how much pressure is at the center of the mass. I propose that the closer a point is to the center of mass, the less pressure per unit mass is on that point. I find that I seem to be able to build this problem up one step of geometric logic at a time.
Step one: two examples
Example 1.
Imagine two bodies, each the size and mass of the earth, and imagine them next to each other (one earth "on top" another earth). The center of their shared mass is at the point between them. Yet, that point has the pressure of only one earth on it (as weighed on the earth).
Example 2.
Or, imagine two other bodies (each of homogenous density): One, the moon; two, a planet with the density of the moon per unit mass, but the size of Saturn (a given unit volume of the moon and this planet is the same in density). Extending down from the surface of this Big Planet is a hole slightly bigger than the size and shape of the moon.
Where is the center of gravity in this Big Planet with this hole in it? Answer: at the center of the mass, which is a little further "down" below this hole than to the center of the sphere of the planet. Also, the gravitational strength of this total mass is less than would be the case if there were no hole.
Now, imagine the moon suddenly materializes into this hole, resting on a bathroom scale at the "bottom" of the hole. As it sits in that hole, the center of the moon's mass is still where it was when the moon was floating free, and the attraction between its own center of mass and the center of mass of the Big Planet determines the pressure on the scale, not the moon as weighed from the surface of a Big Planet that lacks this moon-size hole.
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[ 18 September 2002, 22:08: Message edited by: Danpech ]
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Elend
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Member # 326
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posted 19. September 2002 04:46
people who I suppose are qualified to tell me about the geometric logic of Newtonian gravity have said that the center point of a mass is the point of origin of the gravity of the mass, so that the smaller is a mass, the stronger the gravity per unit mass when standing on the surface of the body [ see http://brp.arc.nasa.gov/Science/Y_GBL/bsc_resrch.html fourth question down ].
If the mass is smaller, assuming the density doesn't change, the volume of the planet gets smaller. Thus the center of mass is closer to the surface. A mass 10x smaller yields a 10x smaller volume, which yields a cubic root of 10x smaller planet radius. Finally the gravity should be 10^(-1/3) that of the bigger planet. This ends up to be 0.464... BUT, note that the Mars density is different ( Mars Data) which leads to a radius about 1/2 of that of Earth. With more exact data the Mars gravity is then 0.107/0.5332^2 = 0.37636 that of Earth. That is about 3/8. I see no error in that 4th question you refer to.
(added that 4th question)
If Mars has 3/8 the gravity level of Earth, does that mean that the planet Mars has 3/8 the mass of the planet Earth?
No, Mars has only about one tenth the mass of Earth. Since an object on the surface of Mars is closer to the planet's center than the same object would be on Earth, the gravitational effect is increased.
[ 19 September 2002, 04:51: Message edited by: Elend ]
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Evan
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Member # 164
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posted 19. September 2002 07:43
This all has to do with calculus, danpech, and really little to do with ISCID. When you are standing on the surface of the earth, every point in the spherical earth is pulling on your with a force inversely proportional to the distance. Each force can be represented by a vector. The resultant vector is found by integrating all those little vectors, and is found to be the same as if all the mass was at the center. This is a consequence of the spherical shape.
If the shape is different (two spheres touching, hole in earth, you are inside the earth, etc.) the situation changes.
It's all calculus.
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bobbyray
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Member # 384
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posted 20. October 2002 22:17
first, i want to make clear i am not a physicist, and have at best a layman's knowledge and training in most of the areas that physics, and other natural sciences, deal with. that said - i do follow the things fairly closely and consider myself not totally useless in these areas. my following comments should go far to seal my fate on this, though, in either direction... ;o)
i think that perhaps gravity *could* be an appropriate topic here, despite the topic starter's concerns, as i am beginning to think that gravity is not so much a basic, natural "force" as it is perhaps an emergent property of certain aspects of spacetime, and that much as the value of "pi" is the result of the ratio of a the circumference and diameter of a circle, the gravitational constant "g" could well have a similar nature, ...of course with an added dimension or two thrown in and the ratio(s) being based on other values...
I haven't yet finished my ruminations on this subject, however i am considering the *apparent* effects of gravity as being due not to a natural force, but rather due more to how the local features or characteristics of spacetime are affected by high concentrations of mass (or mass values) in a relatively small region of space (or in relatively close proximity to each other), and how that could affect the (apparent) movement (with "movement" being simply a translation (or change in the location (values of)) of (an) object(s) along the the statial and temporal axes) of things in proximity to them. I am not suggesting gravity (or the gravitational effect) is not real - to the contrary, the effect is obvious and well described in most ways - however i think our basic approach to understanding it's nature could be faulty (looking at it as a fundamental force as opposed to an "emergent effect"). I think perhaps looking at gravity in a different way could perhaps eliminate it as a problem in certain other areas (for example, GUT's), and may allow some progress to be made where as now it's primarily a roadblock.
to understand what i am getting at, one would need to also perhaps take on a different view of time as well, with it being percieved or experienced differently at various levels of structure or organization, keeping in mind that each *elementary* point-particle or waveform (whichever you ascribe to) has it's own "time values" (among others), and that the values of a larger grouping of such particles (an "object"), or even groupings of such objects (systems), assume sort of an "averaged" value "t" based on the relative positions and motions of those particles of which they are comprised...
- if any of this makes sense to you, then perhaps you can see how this could possibly lead to a view of gravity similar to what i am suggesting...or perhaps motivate you to suggest i inquire as to room availability at the Hotel Bellevue.
anyway, i think this is likely why no gravitons or gravity waves have been - nor will be - detected: they just do not exist. the gravity "effect" is just how we percieve movement, time, etc. in the vicinity of massive objects, or rather how it is manifested, at our level of structure and organization.
i apologize for presenting a literally "half-baked" idea here, however i toss it out mainly in hopes of seeing where flaws in my early thinking on this idea may lie. any takers?
thanks...
(just one request: be gentle...!) ;o)
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brauer
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Member # 398
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posted 21. October 2002 11:15
I have on my bookshelf the slim book A Reparation: Universal Gravitation a Universal Fake by C.S. deFord. It was published sometime prior to 1931 and is a joy to read. I recommend it highly.
De Ford makes some of the same kinds of speculations of the OP, and conducts similar thought experiments. His conclusion? That the earth is flat. (Sidenote: an apparently sincere Flat-Earth Society was extant in Lancaster CA as recntly as 1991).
Not necessarily apropos of your questions, Danpech, but interesting nonetheless.
BTW, in your first example, the force applied to an object at the common tangent of two touching spheres would be twice the "weight" of each of them, not one times the weight.
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Mike B
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Member # 512
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posted 22. October 2002 14:02
Gravity does not act on the center of mass: it acts on every particle of the body in question. For most objects in most situations one can live with the assumption that gravity is acting on the center of mass, as that is much easier to do calculations with. But the reality of how gravity acts is all around us. Here are some examples:
(1) Tides. The gravitational effect of the Moon acts on all of the Earth, not just on the center of mass of the Earth. Bodies of water demonstrate this by being displaced upward towards the Moon (and the Sun, also). The land portion of the surface of the Earth also has tides, but they are so small that it requires very sensitive equipment to measure them.
(2) Silly putty. If you take a piece of silly putty and set it on a flat surface, in a fairly short period of time (hours to days) gravity will flatten it out. Even though the silly putty is a “mass”, gravity acts on all parts of it, moving all parts to the lowest potential energy state possible, given physical and chemical constraints. Everything else does this too, but it is usually difficult to see. Old (100 years +) glass windows will show this, by being thicker at the bottom.
(3) Long things, such as pipes. If you support a long pipe only at its center of mass, the ends will sag. This is because gravity is acting on the entire length of the pipe, not just the center of mass.
This is a great example of why one has to look beyond the model (in this case, the formula of how gravity effects two bodies), however useful it might be, to what is REALLY happening. Ironically, what is REALLY happening often cannot be understood until a good model is developed.
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Mike B
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Member # 512
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posted 22. October 2002 14:22
Danpech,
quote:
But, people who I suppose are qualified to tell me about the geometric logic of Newtonian gravity have said that the center point of a mass is the point of origin of the gravity of the mass, so that the smaller is a mass, the stronger the gravity per unit mass when standing on the surface of the body [ see http://brp.arc.nasa.gov/Science/Y_GBL/bsc_resrch.html fourth question down ]. I don't see how this can be logically deduced from the above formula, and so I take it to be incorrect. It seems to me to be saying not only that a mass has some odd power to transfer its gravity to a single
point at its center, but that the closer to the center of mass is a point, the greater the pressure per unit mass is on that point.
This is a great example of why one needs to understand the assumptions behind and "law" that one attempts to apply, and make sure that they are appropriate for the situation that one is trying to apply it to. It is also a good example of why, when I find myself with two or more "rules" or "laws" that seem to apply, and that seem to contradict each other, I first assume that there is something about the rules or situation that I do not understand, rather than assume that the rules or situation are wrong. Usually I find out that there was something that I failed to take into consideration.
In the case of gravity, Evan is right: it is all about calculus. And there are layers of it. Anything having to do with gravity that isn't written in calculus has a lot of assumptions that you need to be aware of before trying to generalize.
The same is true concerning most other simple statements in science.
[ 23. October 2002, 02:38: Message edited by: Mike B ]
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Danpech
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Member # 163
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posted 17. November 2002 21:21
Thanks for all your fascinating comments. I didn't feel that this matter would generate any interest, but the reason I felt this way had something to do with the fact that my view of it was (now past tense) quite out of the mainstream. But, then, the simple logical science of gravitation is about one of the actual present workings of the physical world.
Relativism, materialism, naturalism, scientism, reductionism. etc. --even supernaturalism--, all have something to contribute to our understanding of reality. But, no one of them can be taken as the magic pill to resolve all questions (none can be taken as the exclusive 'ism').
My thoughts about the logic of Newtonian gravitation were not all correct, and it took me awhile to see this. One of the actually tested facts of Newtonian gravity, and which I was having trouble understanding as to how it could possibly be correct, is that a mass that is inside of a hollow sphere will, in effect, have no gravitational attraction to the sphere, so that, if the sphere is in deep space, the mass which is floating inside of the sphere can be moved about within this sphere without any tendency of this mass to be pulled to the inside surface of the sphere. That is what I was told by gravitational physicists, and I finally understood how it is correct only when I saw how to make a mechanical model of the problem.
Imagine a ring and, imagine, in the center of the ring, a ball. Attached to this ball, and going out toward the ring, are many strings, so that the whole assembly looks like a bicycle wheel. Each string passes through its corresponding hole to the outside of the ring, where it is wound around a tension motor, so that each string has its own motor. The pull which the motors exert on the strings is like the gravity which the walls of the hollow sphere is exerting on the mass that is floating inside of the sphere. The amount of pull exerted by a motor depends on how much string is wound around it (the ball is closer to that motor's part of the ring the more string is wound around the motor). The closer is the ball to one side of the ring, the stronger the motors on that side of the ring pull on their respective strings. But, no matter where the ball is positioned within the ring, it will remain there, because the force of pull in all directions actually equals out.
This gravity problem is just like any problem of truth: unless one sees the whole basic picture of a matter, one's intuition as to what is the truth of the matter itself will be incorrect. Even if one holds as true the final and ultimate ground of all reality. In my case, this is the supernatural.
[ 17. November 2002, 21:29: Message edited by: Danpech ]
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Danpech
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Member # 163
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posted 17. November 2002 21:57
brauer,
You wrote:
"the force applied to an object at the common tangent of two touching spheres would be twice the "weight" of each of them, not one times the weight."
I'm not sure what you mean by twice the weight here, but, imagine a ten-pound watermelon on a bathroom scale. It exerts, on that scale, the degree of pressure we call "ten pounds" in relation to the mass of the earth. Increase the mass/size of the melon, and the 'weight' increases. If, instead of this melon, we have another earth on top of this scale, then the weight will be "one earth in relation to another earth", or, simply, "one earth weight". The pressure on the scale will not be equal to this "one earth weight" times two.
This is also how the pressure per unit mass decreases the closer to the center within a mass we imagine the scale to be embedded. Though the pressure on the scale increases, the pressure per unit mass on top of the scale decreases (that is, not psi, but only the pressure that is exerted in one direction: the direction which the scale is measuring). Or at least, that's what I have been told by Ph.D. physicists, and it makes sense to me.
To all: before I opened this thread, I contacted iscid and proposed my intent to post on this topic, but said that if they thought it was not appropriate, then I would be as happy not to (I was not sure if it was or not). But, they offered me their welcome to post on this topic, per
'complex systems', so that is the reason this thread exists. Just so you know.
[ 17. November 2002, 22:00: Message edited by: Danpech ]
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