• Questioning the Foundations Essay Contest (2012)

  • Inappropriate Application of Kepler’s Empirical Laws of Planetary Motion to Spiral Galaxies Created the Perceived Galaxy Rotation Problem – Thereby Establishing a Galactic Presence for the Elusive, I

Essay Abstract

Astronomers using new, improved spectrographic equipment to study galactic rotation during the 1970s initially presumed that spiral galaxies were 'standard' orbital systems, just like the Solar system, and that the laws of planetary motion should apply. As a result, when the rotational velocities of disk objects were found to be generally flat at all peripheral radii, conflicting with characteristic Keplerian rotation curves, it was concluded that either classical mechanics had been falsified at large scales, or that some enormous, undetected form of matter must be present to extend the distribution of galactic mass to very large radii. The procedural assessment conducted here shows that very large scale aggregations of massive objects cannot be expected to rotate like the highly centralized mass of the Solar system. Newton proved long ago that Keplerian relations specifically apply only to the mass distribution inherent in the Solar system. As a result, no galactic dark matter need be inferred from any discrepancy with Keplerian rotation curves.

Author Bio

Information systems analyst with more than 30 years experience with very large scale systems. Retired in 2005 after 26 years with Federal Express, Technical Fellow, Information Technology, Systems Planning.

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  • Post #2

James,

You do not mention that Newtonian mechanics requires gravity to have an "instantaneous influence at a distance" in solar system distances.

If you read Georgina Perry's essay, topic 1316, you will have noted the term "incomplete information." Incomplete information is responsible for many of the contemporary assumptions, and some of these assumptions are considered as facts. You include a statement about Newton, "Newton proved long ago that Keplerian relations specifically apply only to the mass distribution inherent in the Solar system." Newton admitted he did not know what caused the force of gravity, and he was unaware of the existence of electromagnetic fields, he had, in his time, "incomplete information."

If dark matter has been created because current theory cannot account for the spiral galaxy form, it presents a good reason why this essay contest is needed, to expose the existence of assumptions that have spawned other assumptions.

Your essay does not mention inertia. Newton defined inertia, and he made no distinction whether objects were close or at a far distance. Newton was correct in assuming that the mass distribution of clusters of mass objects, such as seen in galaxies versus a small group of solar system masses, will be different. If one has any concept of how gravity functions as an influence, it seems intuitive that a humongous grouping of mass objects with large spacings will present mass distributions that are more complex than those of a few closely coupled objects.

Had Newton known that the gravitation influence does not have an infinite influence regardless of distance, his proofs and conclusions would have been significantly different. There is a simple way to explain why the gravitation influence is essentially instantaneous in solar system distances, but a person will have to unshackles themselves from the contemporary view that gravity is a curved space phenomenon.

Helical Electromagnetic Gravity

The following statement is contained in the above paper, "Gravity is a two-way process, every mass object is linked to each other by the HEM-HC fields emitted by these objects. The classical definition of "inertia" is applicable for distances that result in essentially instantaneous action at a distance, with delayed inertia, but inevitable, between objects beyond instantaneous distances."

    Frank,

    Please note that I am not a physicist, but an information systems analyst. I have no opinion regarding your objections to Newton's mechanics, but I must point out in his defense that classical physics continues to be extensively and successfully used in a broad range of applications.

    However, my essay is not a defense of any theory but an analysis of the process used to infer the galactic presence of imaginary dark matter by improperly applying empirically derived description planetary motions (not based on any theory) to inappropriate galactic distributions of mass.

    It seems to me that your comments have nothing to do with the subject of my essay. If you have some thoughts about the subject of my essay I'll be glad to try to address them, even though I'm not a theoretical physicist.

    Best wishes to you.

    • [deleted]

    • Post #4

    James,

    What I think Frank was alluding to is the fact that longitudinal EM waves [LWs] provide not only a basis for Newton's action-at-a-distance but also provide a physical mechanism to explain the rotational velocities of galaxies [currently requiring Dark Matter as an explanation].

    Cosmology only recognises Gravity as the force acting between planets and Stars on the cosmic scale - yet Newton's formulation for G [Matter] is essentially the same as Coulomb's formulation for k [charge]. Some concession is made with magnetic field lines on the SUN etc but as Faraday, Gauss & Maxwell all pointed out - you can't have Magnetic fields without their associated Electric fields.

    In short the Cosmos is an ElectroMagnetic environment and it is the E field interactions [of LWs] that facilitate the noted velocity curves, unfortunately cosmologists don't want to acknowledge E fields throughout space so they 'invent' Dark Matter to explain the observations.

    In that sense Newton was correct by modelling the observed motions of planets etc to determine the nett Gravitational force but as EM fields were not known to him at the time he was unable to explain its instantaneous action-at-a-distance force. [it also explains why G & k are so similar in form]

    Any account of Gravitation must take into account all the forces present - Gravitation by Matter, Magnetic perturbations and E field accelerations.Attachment #1: 2_Figure_28.08__EM_waves_800x600.jpgAttachment #2: Figure_71.07__Galaxy_Rotations_800x600.jpg

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    • Post #5

    Abaham,

    Thank you for explaining more fully, and especially for the attached files (I almost missed them) illustrating transverse and longitudinal EM waves and the chart illustrating their suggested conceptual application to galactic rotation. IMO, this chart continues to perpetuate the misconception that galactic gravitation can be evaluated using simple Keplerian methods of approximation suitable for two-body gravitational systems.

    In the terms put forward in the galactic rotation chart you supplied, I argue that gravitation is also 'interactive'. While Keplerian methods ignore the perturbances produces by orbitals other than the one being evaluated, gravitational interactions occur continuously among the massive stars and other objects within a galactic disk. That Kepler's methods chose to ignore them in the interest of simplicity (and specifically their inherent insignificance within the Sun dominated Solar system) - does not physically eliminate their effects. There are an estimated several hundred billion stars and other masses within the Galaxy that, inarguably, continuously gravitationally interact with the Solar system...

    I think that the discrepancy between observed 'flat' galactic rotation and the expected Keplerian diminishment of rotational velocity at increasing radii can most simply be understood by complex gravitational interactions. Each planet orbiting the Sun can effectively be described as a two-body problem - in fact Kepler's equations do so by ignoring all gravitational effects imparted by any other planets, considering only two objects.

    That works fine in the sparse Solar system, where the Sun contains 99.86% of total system mass. Here any perturbances produced by other relatively distant, low mass objects are not often significant. It is primarily the mass of the Sun, through its resulting gravitational effects, that determines the motions of each planet.

    In contrast, from the perspective of each star in the disk of a spiral galaxy, for example, its motions are primarily determined by the vast 'sea' of gravitational effects produced by perhaps millions if not billions of nearby masses. There is no dominating single mass solely determining the motions of all 'orbital' bodies (supermassive black holes comprise a very small fraction of total system mass). Even the collective gravitation of a central bulge does not solely determine the motions of each disk object (some spiral galaxies do not even have a central bulge).

    The complex dynamics of galactic motions simply cannot be solved with a two-body equation! There was no basis for presuming that Keplerian relations should apply to the vast distribution of masses, and vast distribution of resulting gravitational effects, within spiral galaxies.

    I'm quite certain that if the Solar system's mass configuration and spatial distribution could simply be scaled up by a factor of ~200 billion that its rotational characteristics would generally comply with Keplerian expectations. However, discrete stars of nearly 200 billion solar masses cannot exist.

    So, please consider that galaxies are not similar to planetary systems and cannot be expected to behave similarly. It seems to me that there is no justification for inventing some unidentified, undetectable form of mass to reconcile the discrepancy in their rotational characteristics - that should have been expected based on a casual evaluation of their disparate mass distributions!

    In my essay, I've included a "Supplemental Information" section that, under the heading of "Describing Spiral Galaxy rotation without dark matter or modified gravity" lists several reports detailing more appropriate methods of evaluating the dynamics of galaxy rotation, generally representing spiral galaxy disks as - thin disks!

    I do not see any need to look for any metaphysical explanations for the relatively flat rotation curves of spiral galaxies - as I understand, the physics are quite straightforward.

    I can't really evaluate the possibility that longitudinal EM waves account for the observed discrepancy between the relations of rotational velocities and radial distances for planetary systems and spiral galaxies: I think that can be most simply explained by the greater proportions of mass at increasing radii in spiral galaxies. At any rate, if simplistic computational representations of planetary systems are applied to galaxies I suspect the results will be incorrect no matter what forces might be at work.

    However, I am not a physicist - I can only to some extent assess information processes... Personally, I do not find it satisfying that the law of universal gravitation presumes some gravitational force that can be instantaneously imparted at great distances. I also do not find fulfillment in the idea that some curvature is metaphysically imparted to some abstract dimensional coordinates of the 'void' by local aggregations of potential mass-energy. I think that these approaches merely provide useful mathematical representations of unknown physical conditions that allow their evaluation. I think physics should be more physical than that...

    The intent of my essay is to rectify past misinterpretations of observations that have profoundly shaped to future, and now present, of physics. I prefer to reduce requirements for imaginary elements whenever possible.

    P.S. Frank, sorry if I misunderstood your comment.

    Best wishes to you both!

    Sorry for being anonymous - I apparently type so slowly my login expires...

    Abaham,

    I'm compelled to add...

    It is Kepler's quite reasonable empirical conception that the effect of gravitation is 'centrally' directed, as each planet's motions are effectively determined primarily by the Sun. I think the 'interactive' feature described by the 'E field acceleration' conception of galactic rotation is, in essence, correct, but best described as 'dispersed' effects - directly related the dispersal of galactic mass.

    Even in the scenario where 'attractive' effects are at least partly produced by EM emissions, surely their should be some correspondence between mass dispersal and EM emission amplitude and directional effects - similarly to gravity.

    As I understand, there must be some apparently attractive force effect that exactly corresponds to mass, since the relatively cold moon, for example, emits little if any EM radiation of any kind yet produces gravitational effects precisely consistent with its mass.

    While EM attraction effects certainly exist, I'm very skeptical that it is responsible for any significant attractive effect at astronomical scales...

    At any rate, regarding your statement, "Any account of Gravitation must take into account all the forces present - Gravitation by Matter, Magnetic perturbations and E field accelerations," I think this is falsified by the success of Keplerian approximations within the Solar system. Mathematical models are not necessarily required to describe all possible conditions, only those to which they are applied. Ptolemy quite successfully described the geocentric motions of celestial objects for about a thousand years... Similarly, successful demonstration of a mathematical model does not require that it accurately represents all of the factors contributing to the physical conditions portrayed.

    Thanks again.

    Dear James,

    I enjoyed your excellent well-written essay, but unfortunately I don't agree with your reasoning or conclusions. I have an alternative solution with supporting real data for evidence. The galaxy rotation curves can be understood in relation to the many problems with Milankovitch ice age theory. You don't have to be a physicist to understand it, just very open minded.

    Best wishes,

    Alan

    Essay entry: Newtons Isotropy and Equivalence Is Simplicity That Has Led to Modern Day Mass Misconceptions of Reality

      Dear Alan,

      Thanks for your kind remarks.

      Best wishes,

      Jim

      James

      It's clear dark matter is very poorly understood. As an astronomer I've been studying and analysing the evidence for many years, some of which seems even more complex and bizarre than you point out. There are dozens of papers a month published in the MNRAS with excellent new data from the many billions dollars of hardware now exploring haloes. Over half of this is inconsistent with the ruling paradigm, but the round pegs are often still jammed into odd shaped holes none the less.

      The fact is that there is now far better evidence than just gravitational that 'something is out there.' Also CDM semi analytical modelling has helped to a great degree with gravitational matter density distribution, but even they can't model the complexity. (I assume you've studied the millennium simulation, if not do so. An image is in one of the essays here). Galaxy rotation curves are also far more complex than normally assumed, with virial radii related to density where the 'lock step' bodily rotation steps down. There is also much 'kinetic decoupling' now found, where the outer reaches rotate on a perpendicular axis!

      An unfamiliar solution is available with which all the overwhelming 'mass' of observations fit. Of course though it also resolves a good number of related anomalies it doesn't fit the current paradigm or concordance cosmological model so won't be accepted for publication.

      Consider the definition 'dark'. It was only termed that due to low luminosity and diffractive effects. diffuse plasma is now found in abundance. (mainly considered as free electrons). Plasma refractive index n=1 is the same as the vacuum. If DOES however have kinetic effects from coupling and motion (atomic scattering) and can become CO and bound molecular gas, and then be 'seen' (many good HST photo's now on the web). Plasma does of course have gravitational mass, it's thinly spread but there's a lot of space out there. Did you know Earth's own (invisible at most frequencies) bow shock contains billions of particles/c^3m? and the Voyagers have found the Heliospheric shock similar.

      If you'd like an interesting new analysis check out this; http://vixra.org/abs/1102.0016 and please do also read my essay, which suggests the full consistent physical basis.

      It's a crime that far more good up to date research isn't available to the public. Only a trickle get's through, so they have to live off old scraps and a pile of nonsense (not to say most current analysis is not also nonsense). Improvement is on the way in the UK at least.

      Best of luck in the competition.

      Peter

        Dear James Dwyer,

        When eigen-rotational angle of a string is in progressive and regressive variability in cycles, its peripheral end maps a spherical spiral from inside a sphere and represents a spiral galaxy. Ellipse of orbit of each planet around the sun indicates that each elliptical orbit is part of another orbit in the celestial sphere.

        Thus the observable universe differ from actual universe in that the non-observational dark matter described in Lambda-CDM model of cosmology is described differently in a segmental universe as, incoherent cluster-matters for the observer cluster-matter in a locality.

        With best wishes,

        Jayakar

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        • Post #12

        James,

        Abraham did correctly clarify my earlier statements.

        "Personally, I do not find it satisfying that the law of universal gravitation presumes some gravitational force that can be instantaneously imparted at great distances."

        You are correct, nothing is stated in the "law of universal gravitation" that the gravity influence is instantaneously imparted. You will not find any traditional text that teaches Newtonian mechanics mentioning, "Oh, by the way, there has to be an instantaneous influence at a distance for solar system objects to not have spiral forms."

        Unfortunately, some assume the gravitation influence is instantaneous regardless of distance. That type of assumption is based upon "incomplete information". I cite a reference in my paper, The Helical Structure of the Electromagnetic Gravity Field that gives estimates of the influence velocity. It is not infinite, but much faster than the speed of electromagnetic propagation.

        Experimental physicists should be able to approximate the influence velocity, if they look. Measurement instruments will have to be improved to obtain a value that has good precision.

        Supporters of Einstein's gravity theory state that the gravity influence propagates at the speed of light. They are half correct. The electromagnetic (EM) field that establishes the gravity influence does propagate at the speed of light, but the influence, once established, is not limited by the original propagation velocity. The EM gravity field of objects with mass has been propagating for a long, long time.

        The one attachment Abraham provided, Fig. 71.07 "Galaxy Rotations", has the two force equations F, one based upon gravity and the other on charge. For a century now, it is essentially heresy to even suggest that gravity might have an electromagnetic cause. Two simultaneously published papers can shed some light on the issue. The first by Ross McPherson titled, Electrifying Gravity and the second by James Gilson Newton's Gravitation Constant G as a Quantum Coupling Constant

        Einstein's generation never considered the existence of longitudinal EM fields. Unless researchers specifically look for them, using the proper antenna configurations, they will not be able to identify them.

        "I prefer to reduce requirements for imaginary elements whenever possible." You are diplomatic when you use the term "imaginary elements," I use the term "physics fiction."

        • [deleted]

        • Post #13

        I incorrectly stated, "Oh, by the way, there has to be an instantaneous influence at a distance for solar system objects to not have spiral forms." That should be "spiral orbits".

        Frank,

        Thanks very much for the links - they look interesting. I do think that the physical processes responsible for producing gravitation have not yet been identified, much less fully described.

        I focus primarily on the process used to infer the presence of galactic dark matter because, as an information systems analyst, it's relatively straightforward and seems so obviously in error. I can't understand why no one seems interested, but I do know that if I can make any useful contribution to physics, that's it!

        Peter,

        Since you referred me to both your FQXi essay and a separate research report in your preceding comment, I'll respond here. I'll apologize in advance for being blunt, but I think there's some important issues that must be addressed.

        As a lay information systems analyst I cannot reasonably assess your essay, but I am compelled to point out a critical misrepresentation of the right image in 'Figure 1'. The superimposed image caption states: "Visible 'Dark Matter'. Galaxy Cluster CL 0024+17."

        The Figure 1 caption states:

        "Space. Different constituents of the Inter-Galactic Medium (IGM) are visible at each waveband. X-ray (left) and visible (right) 'dark matter' around clusters, galaxies and stars. The 'clouds' represent a diffuse plasma medium of ions, CO and molecular gas..."

        It's not clear what 'clouds' you're referring to, but I'm certain that the so-called "visible" dark matter is not visible in any waveband. As briefly explained in Wikipedia - CL0024+17, the image shown in your essay attributed to "visible" 'dark matter' is actually a composite telescopic image overlayed by a 'gravity map' illustrating dark matter as it seems to be inferred from identified gravitational effects. Those gravitational effects are very tenuously identified from minute optical distortions of likely many thousands of background galaxies, statistically evaluated to derive the location of the weak lensing medium. The total mass required to produce the identified weak gravitational lensing effects is compared to the estimated mass of the clusters' galaxies and the intracluster medium (thought to represent most of the cluster's mass) - the difference is thought to be the mass represented by the inferred dark matter. This exceedingly complex process is subject to significant error.

        The illustrated CL 0024+17 dark matter is not visible, and cannot consist of any ordinary detectable matter and does not emit any EM radiation including X-rays. Since this identified peripheral dark matter ring circumscribing the galaxy cluster, conveniently aligned to the Earth's line of sight, is thought to have been dispersed by some collision, it is not collocated with the hot, X-ray emitting intracluster medium. Hubblesite (no relation) contains a newsy discussion and interviews, concluding with the statement: "Cl 0024+17 is the first cluster to show a dark matter distribution that differs from the distribution of both the galaxies and the hot gas."

        The Wikipedia entry referenced above includes both the unaltered telescopic image of CL 0024+17 and the illustration overlay you described as "visible" 'dark matter', for ease of comparison.

        Regarding your paper you referred me to, http://vixra.org/abs/1102.0016, its "Fig. 1" image of NGC 5128 exhibits some 'pixelating' distortions. ESO Centaurus A is a much clearer image showing the illuminated area from the disk to the ends of the polar jets. These seem reminiscent of the giant polar bubbles of plasma recently detected in the Milky Way, thought to have been ionized by relativistic jets when the Milky Way last had an active galactic nucleus. Your paper states: "The dense ionised particle plasma halo is the dark matter that binds the galaxy together gravitationally." I'm not sure whether you're referring to the apparent illuminated polar bubbles or the apparent dense molecular clouds surrounding the disk periphery, but in neither case could they compensate for a the absence of a Keplerian rotation curve (one whose plotted rotational velocity diminishes at increasing radii).

        Keplerian relations produce planetary rotation curves that are flat for the planets nearest the Sun; for planets at increasing radii, their rotational velocity continuously diminishes. For dark matter to produce the relative flat rotation curves observed for visible galactic disk objects, it is necessary to significantly extend the galactic periphery, increasing total mass by up to a factor of 10. This configuration requires that most of the galaxy's diameter is composed solely of undetected dark matter. There is no matter shown in the Fig. 1 image that could produce this configuration. Dark matter must be undetected. The ESO has produced an artist's impression of the Milky Way galaxy's dark matter halo to illustrate the necessary mass distribution required to produce observed rotational velocities within the context of Kepler's laws of planetary motion applied to spiral galaxies. Please see: ESO DM Halo.

        Of course, if you read my essay you should have found that I argue that imposing the specific laws of planetary motion on vast spiral galaxies is invalid, and artificially produces the falsely perceived galaxy rotation problem that seems to require the compensatory mass thought to be provided by imaginary dark matter. As shown in the "Supplemental Information" section of my essay, there are a number of physicists that have produced models of spiral galaxies that accurately describe their observed rotational characteristics without requiring any dark matter or modified gravity.

        Best wishes.

        Frank,

        I finally read through the reference link you provided in your first posting: Helical Electromagnetic Gravity. Not having an education or background I do find some things too difficult, but I do the best I can. I found your report very interesting an enlightening, although I certainly couldn't understand enough of the details to be able to assess the proposal's correctness. I've also attempted to read the other two references, with little success, I'm afraid.

        The one thing I find is that it has also seemed inescapable to me that the two principle working theories of gravitation do not even attempt to specify what physical elements and processes produce the effects that they so usefully describe. In other words, applying curvature to abstract dimensional spacetime coordinates ingeniously explains only the results of some physical process - but not what the physical process was! Likewise Newton's undescribed force of attraction.

        Without actually determining the physical processes and elements actually involved in the production of gravitation's effects, it's impossible to really understand the effects of gravitation in very different conditions than those we experience. For that reason alone I applaud any efforts to understand the physical nature of gravitation.

        However any EM conditions and processes are proposed to produce some or all of the gravitational effect, they must explain how the effects of gravitation consistently relate to the mass of an object rather than any energy state. For example, the effects of gravitation seem to be identical relative to their mass whether it's the Sun or the Moon. Certainly the Sun is a high energy emitter of EM radiation while the moon is not.

        As I have said, I think that the crucial issue identified in the referenced "Galaxy Rotations" chart is that "Newtonian gravitation" (actually Kepler's laws of planetary motion) is perceived as describing only a central attraction. As I referenced in my "Supplemental Information" section, several physicists have produced models successfully describing galaxy rotational characteristics without relying on any simplistic centralized attraction. For example, please see: Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. The chart is also incorrect in stating that "Gravity can only produce spheres or ellipsoids" - it obviously also can produce spirals galaxies, and the gravitation of interacting galaxies is 'interactive'.

        The Galaxy Rotation Problem was erroneously manufactured by applying Keplerian rotation curves to spiral galaxies (as shown in the "Galaxy Rotations" chart Abaham referenced). That error does not actually represent Newtonian gravitation, as shown in my reference above. It's interesting to me that whoever produced that chart also recognized that it was (the idea that) gravitation's effects are only centralized that produces the requirement for galactic dark matter.

        While I think it is important to understand the physical nature of gravitation, whatever it might be, I think it's far more crucial at this point in time that physics recognize that galactic dark matter was erroneously inferred, and most likely does not exist in any significant quantity.

        9 days later

        • [deleted]

        • Post #17

        Jim,

        Great work as usual.

        One question: If you are not correct, then it's possible that dark matter might exist. Since many galaxies have flat rotation curves, and given the fact that these galaxies don't all have the same mass nor do they rotate at the same velocities, what are the mathematical odds that each of these galaxies would conveniently contain just the right amount of dark matter for them to individually produce this specific rotation behavior?

          Chris,

          Great question. For all (especially spiral) galaxies to have just enough dark matter to produce a generally flat (or even increasing) rotation curve rather than the inappropriately expected diminishing curve, there would have to be some feedback mechanism at work in the development of galaxies such that the amount and/or the distribution of ordinary mass would just fit the amount of dark matter present - or vice versa, that a specific amount of ordinary matter developing into a spiral galaxy would somehow collect the specific amount of dark matter necessary to produce a nearly flat curve.

          Moreover, the different fundamental types or morphological classifications of galaxies, sphericals, ellipticals and spirals, early and late types, each seem to have varying amounts of dark matter that would have to be present in order for their observed rotation curves to fit with Keplerian methods of determining rotational velocity.

          For example, nearly spherical galaxies seem to require the least amount of dark matter, while more elliptical galaxies require a little more, and spirals require an even greater proportion of dark matter. The amount of dark matter thought to be required generally increases as the mass configuration of ordinary matter increasingly deviates from spherical symmetry. To this extent, the amount of dark matter required to explain a galaxy's deviation from Keplerian rotational characteristics is related to the extent of its deviation from spherical symmetry.

          This seems problematic, since the different types of galaxies are thought to represent evolutionary stages of galaxy development through mergers. For each type to have the specific amount of dark matter present to explain the deviation from Keplerian expectations, galaxies would have to gain or loose a specific amount of dark matter during the merger and eventual reconfiguration...

          Alternatively, of course, these variations in dark matter requirements actually result from Kepler's relations and resulting equations being derived solely from observations of the generally spherically symmetrical mass distributions characteristic of the Solar system - when inappropriately applied to complex aggregations of billions of massive objects.

          As I said - great question!

          7 days later

          • [deleted]

          • Post #19

          Hello James,

          The reasoning in your essay is quite interesting.

          I haven't read the papers you mentioned in the appendix of your essay, but the central section of your essay, "Establishing Requirements for Galactic Dark Matter", contains no references to earlier publications with the same argument. So my question is: is this reasoning entirely yours?

          If so, you might want to pursue the issue further and discuss it with some professional astronomers; I wouldn't approach those who have made a name with dark matter research, but perhaps the ones mentioned in the appendix of your essay find it interesting. You might be able to get a full journal article out of it with a valuable point.

          Best regards, Marcoen

            Hello

            Thanks for your very supportive comment. I have read some related unpublished remarks by C. F. Gallo referring to the initial misconception of galactic dark matter, although I arrived at these ideas independently and have developed them much further. J. D. Carrick and F. I. Cooperstock make some brief mention of the same issues in their unpublished paper referenced in my essay. I had previously discussed those points in emails to one of them. I have had some fairly extensive discussions with a number of the authors of my references, including directing them to this and somewhat similar previous essays. However, while the discussions have been very favorable, none have addressed the specific points made here.

            I approach this problem as a highly experienced (retired) information systems analyst. Somehow I get the impression that physicists may have a wholly different perspective - and tend to dismiss my analysis (I cannot produce any mathematical proofs, etc., although they are certainly achievable to someone more capable).

            I also suspect that there is a great deal of professional reluctance to so directly criticize the established work of a so highly regarded astronomer as Vera Rubin, not to mention the many thousands of researches that have published works presuming the existence of galactic dark matter over the past several decades. I have unsuccessfully attempted to contact Vera Rubin directly several times during the past few years.

            I do appreciate your interest, but don't feel that I'm capable of producing a paper that would be accepted for publication. If you would be interested in further developing this line of reasoning - I would certainly consider a collaboration!

            Sincerely,

            Jim