Contradicting Newton's Shell Theorem - a note offered the forum for 'peer review'.

The following is presented as a follow on to a previous 'gravity below the surface' thread that ended in the cess pool and is offered to the forum collectively for a peer review.

Mass-force-centers in stellar spherical shape may not be considered located at the sphere mass center relative to an external mass m
Geistkiesel 4/2009​

1. IntroductionThe following is a short note regarding the location of mass-force-centers in mass-attraction physics using only the assumptions intrinsic to the universal law of gravitation expressed as F = - GmM/r^2. From this I conclude that the results are incompatible with Newton’s Shell Theorem (NST).

The results indicate at least four erroneous conclusions critical to Newton's Shell theorem, beginning with the finding that the total mass in a spherical stellar object may not be presumed concentrated at a point located at the sphere center of mass (COM). This is arrived at from observation of the fact of the physical extension of spherical objects which means the hemispherical mass closest to a test particle m1 will apply greater force than the hemispherical mass farthest from m1. This observation, of course, requires the mass-force-center location to be offset from the sphere center in the direction of m in line with the m1-M axis, thus precluding the result of NST that states that the total mass of the sphere acting on m1 external to the sphere may be considered concentrated at a point at the spheres’ mass center.

Second, the use of vector notation is improper and does not represent the physical circumstances described in the development of Newton's Shell theorem. The link below (thre are others) describe in various ways, that the speed of gravity Vg > 10^8c, and some offer that the speed of the force acting mutually on m1 and M is instantaneous - an analogue to Einstein-Podowski and Rosen forces inferred in the famous PDR experiments.

For an intro to this subject see the link:
http://en.wikipedia.org/wiki/Speed_of_gravity

Expecting some opposition here, consider the effect of the sun’s ‘speed of light’ pull on Jupiter that then radiates the effect the force back to the sun. The conservation of angular momentum principle would result in a solar system unrecognizable from today’s regulated state of benign equilibrium. Hence, as m1 and M are observed to react to the mutual forces acting between the two masses, the forces must be confined as local forces restricted to the boundaries of the two masses all of which precludes using vector analysis regarding the description of the attracting forces.

Thirdly, and this is in line with the concentration of the mass-force-centers (MFC) erroneously placed by NST at a point coincidental to the COM of the sphere. The mathematically induced concentration of MFC to a point ignores the physical extension of the masses, m1 and M, and the effect of the forces located at varying points within the masses. If a small mass m is located at the midpoint of two much larger masses, say two black holes, the vector maths tell us that the forces on mare a net zero, when the forces, if large enough, could rip apart the mass of m. I say, if the two opposing masses are pulling at 100 force units each, that the total force acting on the structure of m is 200. This is not a matter of simple mathematical semantics.
Therefore, NST’s result of the concentration of MFC at the COM of the sphere using vector analysis shows no real physical structure of the masses involved primarily through the misuse of vector analysis.

2. Measuring Mass Force Centers [attraction] between m1=m2=m3=1 along a common axis.For m1 = m2 = m3 = 1 unit mass, and G = 1 unit gravitational constant, and with r = distance between m1 and m2, the force of mass attraction is, F12 = 1/100 for a separation of r = 10 unit distances (ignoring the negative sign throughout).

F13 is the force measured between m1 and m3 for a separation of 12 unit distances, F13 = 1/144.

3. Locating the Mass-Force-Center of combined m2 and m3 relative to m1.

The total force of F12 + F13 = F123 = I/100 + 1/144 = 244/14,400 = 61/3200.
To locate the MFC of the two masses with respect to m1 we use the expression M = m1 + m3 in the force expression as above only now we see that M = 2 and F = GmM/r^2 = (1)(1)(2)/r^2 = 61/3200, or r^2 = 6400/61 = 104.1.

Therefore, r = sqrt(104.1) = 10.20 or in other words, 11 > r > 10. The force center is not at the mass center of m2 and m3 which would be located at 11 if it were.

The center of mass-force of the two particles is not located at the center of mass of m2 and m3, but is located offset from the mass center (center of gravity) in the direction of m1 at approximately 10.20.

Here, F12/F13 = (1/100)/(1/144), or F12 = 1.44F13. If there are two masses in line, or umpteen trillion in line with m1 the principle is the same. In the skin of the shell models, each force addition in such theorems must take into account the asymmetry of the each differential mass, dm, located on the shell, that to an observer at the shell center only, all is symmetric regarding the distribution of mass. This is not the case for a mass located outside the shell where the forces are subject to the inverse distance square dependence of the relative locations of m1 and M shell mass.

The fourth objection to NST is that an object within the shell located off from the COM will experience an imbalance of forces due to the sum of the individual differential masses on the sphere, hence forces, from the total surface of the sphere act on m1 inside the sphere asymmetrically and certainly the forces on such a mass is certainly not zero – to arrive at this erroneous conclusion requires the formation of vastly differing laws of mass attraction on objects located within spheres – the fact that there are no such animals will not be used as an argument opposing NST. The circumstances for mass forces (MFC) on objects within solid spheres offer similar objections to those offered here regarding NST.

Consider the mass attraction calculations that gave birth to the ‘dark matter’ scenario – certainly, a reversionary scrutiny of this concept is three hundred years overdue.
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You failed to contradict Newton's shell theorem. In fact, from your confusion of physical fact, non-Newtonian theories of gravity, and erroneous statements, it is clear that you do not understand either Newton's early work which led to the modern notation of vectors or to the famous theorem itself.

This, in spite of numerous attempts of educators and numerous corrections to previous misstatements made on your part.

 

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Do you agree that F = - GmM/r^2 expresses the universal law of gravitation?

Do you agree that if m1 = m2 and m1 is located 10 distance units from m01, and m2 is 12 units from m02, and if m01 = m02 then the force of mass attraction for m1 and m01 is greater than that of m2 and m02?

You must agree with the above, and then you must agree with the physics described by F = GmM/r^2 which dictates the answer to the two questions above. This being the case you must agree that the force of the closest hemispherical segment of m1 contributes a larger share of force of attraction to the total force acting on m01 than that contributed by the hemisphere of m1 farther removed from m01.

This being the case then, NST falls before the seminal notation of the force expression has been scribed onto a written surface. NST falls/fails for the simple reason that the above couple of sentences stating that F, being an inverse square of the separation distance means, that when equal masses distributed asymmetrically [as in the nearest and farthest hemisphere of m1 from m01] to a test mass that the mass associated with the smallest number in the denominator of F contributes the greater force in the mfc relationships.

The notation in the thread title is consistent with the thread being submitted to a ‘peer review’ by the membership of sciforums. If your effort here was made in the sense of a peer review then I thank you graciously for your input. I must comment that your post was starkly physics free in content, which is just my opinion.. ​

 

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who ever said it was?

 

you are making it all so much harder than it really is. all you tave to do is picture it in terms of lines of force and it becomes obvious.

 

Newton's Shell Theorem said so.

 

a dipole is not a shell. 2 different things.

 

The opening post discussed the instantaneous nature of mass force centers that discounts the existence of a field in the space separating the masses. This being the case, vector math will not do the job and the lines of force you discussed do not exist - that is if the speed of motion of the forces is instantaneous, there is nothing remaining in the space between the objects describable with lines of force.
You said "it becomes obvious" What is obvious?

 

What dipole are you talking about. The shell I was talking about was Newton's Shell Theorem - have you ever heard of it?

 

the finite speed of gravity results in gravitational waves. that does complicate things slightly but that has nothing to do with your assertion that one cant calculate the force between 2 objects by treating them as point masses. at least, not in the case where they arent moving relative to one another.

 

the 2 masses represent a kind of dipole. a shell is definitely not a dipole. rules that apply to one cant be applied to the other.
the shell theorem is perfectly obvious if you just picture the lines of force involved.

 

I disagree strongly. Let me attempt to indicate how much in error with unambiguous laws of physics your statement is. My argument is not tricky or complicated and requires no verifiable experimental results.

You are aware that universal law of gravity is expressed as F = - GmM/r^2 and that the inverse of the distance squared has a very clear physical meaning. We have three masses m1 = m2 = m3 and set m2 10 units from m1 and we set m3 12 units from m1. I am not being condescending by reminding you of 5th or 6th grade (school year) level math which says that the smaller a denominator of a fraction the larger the number becomes. When the denominator is squared the smaller number takes on even more strength as a large number.

If we put m1, m2 and m3 in a axis-line at the distances indicated m2 has the smaller denoimnator than m3 hence m2 will calculate as the larger contributor of mass-force than m3. I am treating all the masses as point sources and when calculating the point from which m1 experiences the force of both masses, the point of the mass-force-center will be at 10.2 which is not the center of mass of m1 + m2.

In the case just described you are correct and the masses may be considered as point masses, however, there will be a lingering error if we so treat the masses as point sources.

For example, the center of mass for m2 and m3 is located at the midpoint of the masses and in the present condition the COm of m2 and m3 is located at 1 [m2 at 10, m3 at 12]. If we calculate the location of the total force contributed by m2 and m3 on m1 where all masses are thee same, G is a unit constatnt and all F = masses are unit mass = 1, then the combined force is F = G1(1 + 1)/r^2 = 1/100 + 1/144 and r is located at 10.2, which is more accurate a determination that assuming the combined mfc originate at the COM, or at the poinjt marked as 11.

However, there is still an error in my calculation for a very obvious reason.. The hemisphere of mass closest to m1 contributes a greater force on m1 than does the force contributed by the hemisphere of m2 farther from m1 and similarly for m3. If we chop m2 (and m3) into eights, for instance, and string these reduced masses (but not points) along the m1-m2 axis for a distance equal to the diameter of the sphere m2, we see immediately that the mass-force-center is located offset from the point 10 in the direction of m1 along the axis. However, the error in this latter case is much reduced from that considering all three masses as point masses.

I cannot emphacise the point sufficiently that asymmetry of the mass distribution of m2 with relative to m1 must be taken into account as I have been shouting out loud in this forum.

The question the astronomers and astrologers need to ask themselves rhetorically is, "what degree of resolution do I require for the particlular problem being considered?"

For instance, Granpa [I was so annointed in August of last year, when my daughter gave birth to Jasper Alexander Cronin, AKA 'the Shark' - eating habits, or "Tiny" - when first seen, or ' Jac' - all three of which are consistent with one Granma Irish, the other Jewish, both Granpas Irish with percentage running from 1/2 to 1/2+ - [I trust this diversion didn't throw you off did it?], and only if you are familiar with the problem - I vaguely remember that the first criticism I was aware of re 'dark matter where a star was erroneously considered a part of a galaxy under scrutiny - that was not a part of a galaxy being monitored this star was tagged with the identification as an 'interloper', but when seen through the galaxy center was actually located some distance external to the galaxy - the far side - . This misidfentified star's trajectory- velocity was measured too high thus prompting the speculation that unseen dark matter must be responsible for the excess in velocity. If you are familiar with the overall question of dark matter maybe you could inform us of the effect of utilizing the corrections in locating the mass force centers for galaxies, super-clusters etc suggested here.

Just to keep the thread on track, this thread is titled as contradicting Newton's Shell Theorem which, beside the errors in physical assumptions used in developing the theorem, including consaidering the forces as vectors extending in space is some conic volume appearing as an ice-cream cone with the farthest hemisphere from m1 being an idealization of the extension of mass.

To conclude here,stellar masses are never seen in the real world. as point masses - reality means physical extenskion- point masses are convenient and error prone models that offer nothing save distortion to the advancement of the language of physical law - math has its place and must not be confused as an equal and appropriated use of the word physics. In this same line of reasoning, the confidence placed in mathematical models should be clearly differentiated from the public reputation of the authors. Newton is one of those "giants" whose sholders I and you are standing on, or so I am told. Just don't expect me to grant Isaac an uncritical adoration and acceptance of his work because of the reputation he enjoys aftyeer all he has been dead for three hundred years. You may disagree with my analysis in this thread but you do not seem the kind of scientist who quotes from the gospels of Saint Isaac, Saint Gallileo and Saint Kepler as if their works are indellibly cast in high grade stainless steel. Isaac had a reputation as a plunderer of other's work product, he insulted Leibninz with the sham panel he formed to fairly determine the true and original author of calculus - S Hawking quotes Isaac as "It felt so good to break Leibninz's heart". After his appointment as Chancellor of the Exchequer Isaac set a record for hanging counterfeiters of the realm's coin.

The instantaneous nature of the mass-force-velocity prohibits observing any force in the space separating the masses, which would ring loud and clear to use a mathematical model oither than vector analysisfor as a shorhand describing the physics of the matter.
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The Shell is certainly not a dipole and I have not treated it as such. I hav
e treated the shell and solid spheres as exhibiting the extension of mass and together with the ibverse square effects of F = GmM/r^2 the masses associated with Shell and the dipole are all asymmetrically distributed with respect to the test particle - to repeat: the hemsiphere of the shell (the closest entity constituting the dipole) contributes more force to the test partilce than does the hemisphere located farther removed.

Granpa, do this. Draw the rings on the shell surface as the model;s on the internet show. Draw two rings of equal radius where one ring is in the closest hemisphere to m1 and the other farther from m1 located in the farthest hemisphere. Draw your force diagrams, and vector models and ask yourself:" Does the mass-force-centers on both rings contribute equal mass-force-centers relative to m1?

Then look at the development of the theorem where the integral is taken symmetrically with respect to the observer in the center of the sphere - if you haven't seen the errors in your ways yet, then I suggest you get your moinney back from those who took your money in exchange for a stilted mathematics education - I am npot an an gel, oh no, I've led a full life, drinking, gambling and once, I talked back to my first wife - yes, I am not without my own scars, I am just one of those who altereed his perspective and you kinow what? I didn't have to seek or receive permission to develop my own vision.

 

You've tried this nonsense once before. Learn some math.