van Maanen's "Unsupportable" Internal Motions
[Added on 26 July 2003]
van Maanen's critics err! Object image sizes are not the limiting factor
regarding the precision in astrometrically locating salient points on
astronomical plates, for example, the centroids of object images.
According to the History of Leander McCormick Observatory web page,
in 1916, the Gaertner Single Screw Measuring Engine allowed an operator to
read positions down to about 0.003 arcseconds on plates taken with a 40
Van Maanen used a 60 inch telescope for the majority of his work.
Figure 1 shows that position measurements can be made down to dimensions
much less than the diameter of blurred stellar images. Figure 1a
represents a section of an early photographic image, and Figure 1b
represents the image taken a suitable number of years later. It should be
obvious that delta X and delta Y can be much smaller than the atmospherically
blurred diameters of the stellar images.
Illustration of Astrometric Measurements Smaller than Atmospheric Seeing Limit
Present day. - CCD astrometry has demonstrated 1 milliarcsecond positional
accuracy (Monet et al. 1992). This level of precision means that proper
motions of distant objects can be determined on time scales of 10 years or
MD&SP) (CCD photography does not get rid of atmospheric blurring. It
allows you digitally dig into the fuzzy stuff without the mechanical
idiosyncrasies of the measuring engines.)
See: On Spiral Nebulae, van Maanen et al..
* * *
Contradictory Reports on Lundmark's Findings
Added on 13 July 2003
There are unresolved differences of opinion about the results of Knut
Lundmark's re-reading of van Maanen's plates for M33. Listed here are two
quotes from recent critics of van Maanen's "rotations."
In his section on "The Island Universe Theory," Kurtiss Gordon
"Although his results correlated well with van Maanen's with respect to
direction and relative size of proper motion, the absolute scale of
proper motions was less than 1/10 as large as those van Maanen had measured."
An "Anonymous Critic"
"The Swedish astronomer Knut Lundmark also acquired evidence that van Maanen's
evidence was faulty. He was allowed to remeasure the very same plates used by
van Maanen to determine the motion of M33. In 1924 he found completely different
results, namely that there was no measurable rotation of M33's image in the five
year interval between the plates. In other words, van Maanen's claims were completely
bogus. Lundmark told some of his colleagues privately of his results. He also published
a paper to the same effect in 1925, but it was either too obscure or too polite to cause
many other astronomers to notice."
The following table shows a comparison of van Maanen and Lundmark's
measurements of motions in M33.
Table added 26 Oct 2003.
Readers may read Lundmark's obscure 1926 report
(LK26) in the Astrophysical Journal.
[Added 05 October 2003; updated 26 October 2003.]
- - -
See Gustav Holmberg's article
Astronomy in Sweden 1860-1940, Uppsala Newsletter: History of Science nr 26 (1997), for a
commentary on Lundmark's work on spiral nebulae. (Comments are in the fourth and third paragraphs from the end.) [Added 27 September 2003]
Hubble's Demolition of van Maanen?
[Added 1 August 2003]
Michael Hoskin summarizes the warfare between Hubble and van Mannen (HM97).
He says: "The van Maanen problem became acute as the Dutchman pointedly
persevered with his comparisons of pairs of photographs of spirals,
concluding in every case that the nebula was rotating at a speed that made
it physically impossible for it to be an island universe."
The warfare seemingly ended in 1935, with Hubble winning. Hoskin
reports "A compromise was imposed, and in 1935 readers of the
Astrophysical Journal were no doubt intrigued to find there a
two-page paper by Hubble delicately outlining his conclusions, immediately
followed by a two-page paper by van Maanen, conceding that 'it is desirable
to view the motions [the rotations in the spirals] with reserve.'
The author would hope that Hoskin's purpose was to encourage readers to
read the papers for themselves, because although what he says about the
papers is true, may be misleading. Hoskin makes it sound as though Hubble
demolished van Maanen's findings and that van Maanen's new tests put
him in his proper place. That's not quite like it was!
Hubble's four paragraphs and single ambiguous tabular summary
no substantive data to back his claim for non-rotations. He fails to
explain the relation between his total observed displacements and what
he calls extrapolated rotations. The text reads as though he
vectorially added the motion vectors of individual nebular points to get his
total observed displacements. (Such a process would, in fact, tend toward
zero, but the result would be meaningless.) In three cases he relates
negative total observed displacements to positive extrapolated
rotations (which were supposedly of a much smaller order than the values
van Maanen had been "finding."). In four other cases null values for
total observed displacements are related to positive extrapolated
rotations. It is very hard to tell just what Hubble was reporting, other
than that he still didn't like fast nebular rotations. [This paragraph will
in all likelihood come to be toned down.]
In regard to van Maanen's supposed declaration of surrender
he stated "The measures give motions for both nebulae [M33 and M74]
in the same direction as those found for the spirals measured previously;
but the value of M33, mean of 114 nebular points, is considerably
smaller (+0.013 milliarcsec as compared with +0.020 milliarcsec) than that
found before. " The phrase considerably smaller was the
politically correct thing to say, and was probably part of the
imposed settlement. On the other hand his new smaller value for
M33's rotation was a hefty 65% of his 1921 measure. (Reading
between the lines is encouraged.)
This writer has not had opportunity to do a good literature search to compare
current findings on spiral nebula rotations, compared to those reported by
van Maanen, but is of the opinion that the findings will match up just fine.
If they do, then the constant rotation curves for spiral nebulae, a.k.a.
"galaxies" can most likely be explained in terms of plasma dynamics.
[A paragraph, duplicate to that preceding the section on "Contradictory
Reports on Lundmark's Findings," above, was removed on 18 Sep 2015.]
* * *
But What About Hubble's Redshifts?
When Hubble and Humason first announced their systematic redshift-distance
findings for spiral nebulae, Humason cautioned their colleagues that what
they were calling apparent radial velocities might not really be
velocities. He explained that because they didn't have a new word or phrase
to apply to the newly discovered phenomena, they took the
already-in-use phrase apparent radial velocity and used it in
conjunction with their redshift measurements. [This may not be said right.]
[Humason's actual words on the subject:]
"It is not at all certain that the large red-shifts observed in the spectra
are to be interpreted as a Doppler effect, but for convenience they are
expressed in terms of velocity and referred to as apparent velocities."
(HM31) Page 35.
[Added 25 Oct 2003.]
When Hubble's redshift-distance relation is applied to the Virgo "Cluster"
of galaxies, the cluster appears to be elongated along a line that
passes through our Solar neighborhood. Goodman says this causes the
"Copernican Problem." (GJ), i.e., it puts us into a preferential reference frame.
(GJ Link no longer works.)
"Instead of immediately recognizing this as a problem, the mainstream adopted
these configurations, calling them the "fingers of God."
(GJ) This effect is sometimes called a redshift-space distortion.
The Copernican Problem
Louis Desroches says it this way.
"Two important effects occur in redshift space. Although redshift
corresponds to true distance according to the Hubble Law, small peculiar
velocities not associated with the Hubble flow can cause distortions in
redshift space. The most evident of these is the Fingers-of-God effect,
where long thin filaments in redshift space point directly back at [an]
observer. We should know by now that we are not privileged observers,
this effect must be unphysical."
According to P.J.E. Peebles, Zwicky and Smith found the velocities of
individual galaxies in the Coma and Virgo Clusters were about a factor
of ten to 100 larger than they expected. (DJ) -
(Link to www.astro.queensu.ca no longer works.)
This "Fingers-of-God" effect can be seen in Figure 3, which shows the
elongated shape of the Virgo Cluster. (The Coma Cluster might be in there
The idea behind cosmological redshift is that spectral elements from
remote locations (in other galaxies/spiral nebulae, for example) were
generated at essentially the same wavelengths as for local sources, but
were somehow shifted. (Originally it was supposed to be a Doppler
shift; nowadays it's politically correct to say that it's caused by an
expansion of space.)
Virgo Cluster in Redshift Space
In 1938 Hubble
wrestled with two viewpoints on the origin of cosmological redshifts. The
first was that the universe (the small part of it that we could see) was
stationary and homogenous and the redshift-distance relation was linear,
however we did not know the non-Doppler cause of the observed redshifts.
The second viewpoint was that the universe was expanding (the spiral nebulae
were receding from us) but that the distribution of matter was no longer
uniform (the density increases outward), and the law of red shifts is no
longer linear (redshifts increase with distance at an accelerated rate).
A Variable Charge Explanation for Cosmological Redshift
Regardless of the manner of how light gets cosmologically redshifted, the
redshift, as currently understood, is tied to the unverifiable
assumption that the unit electrical charge (the charge associated with
electrons and protons) is a space-and-time constant, even in the remotest
parts of space and at the longest times ago.
In 1988 the author published a (non-mathematical) hypothesis
(FR88) that electrical
charge is not constant, rather that it is a matter-density-dependent
In quantum mechanics, the wavelengths of emission or absorption lines in
spectral series are proportional to the inverse fourth power of the
unit electrical charge If electrical charge in a given region of space
is different than locally then we should expect to see all of the spectral
elements from that region to be shifted in a systematic manner. (The
fine-structure constant, which is proportional to the fourth power of the
unit electrical charge, may also come into play here. This is because
the internal spacing of individual lines within spectral multiplets is
proportional to the fine structure constant.) An observed set of
redshifted lines thus becomes an indirect measure of the ambient
... matter density in the source's region of space. [The word local
was replaced by ambient on 14 Apr 2007.]
(See the redshift derivation in Figure 4.)
[Figure was revised on 13 Apr 2007.]
Variable Charge Redshift Z as a Function of
e(remote) and e(local)
A "GIGO" function for the absorption-driven emission of force carrying
particles, positive and negative charglets, in the author's ...
Emission-Absorption-Scattering sub-quantum physics model
provides a theoretical framework, which allows (demands) charge to be a
material density dependent variable.
"Ambient matter density" as used above, is related to the total
mass in a volume of space on the order of one cubic light year or less.
* * *
The [pdf] article, Does the proton-to-electron mass ratio mu = Mp/Me
vary in the course of cosmological evolution?
may bear a relation to the prospect of electrical charge being a
cosmological variable. It touches on some of the same consequences, for
example, anomalies in quasar redshifts, which would ensue if electrical
charge were to be cosmologically variable. [Added 07 Aug 2003.]
* * *
The author's variable electrical charge hypothesis for explaining anomalous
redshifts is similar to the Narlikar-Das Variable Mass Hypothesis (VMH),
based on the Hoyle-Narlikar theory of gravitation. Arp has incorporated
the latter approach in his reasonings on anomalous quasar redshifts.
One primary difference between the two approaches is that the author's
variable charge wavelength changes are proportional to the inverse fourth
power of the local-to-remote differential in unit electrical charge,
whereas for the variable mass hypothesis the changes would only be
proportional to the inverse of the first power of the local-to-remote
elementary particle mass differentials. (See the redshift derivation in
Figure 4, Part 5.) The two approaches are not mutually exclusive.
[Added 20 October 2003.]
See Bill Keel's commentary
touches on Arp's handling of possible close relations between
Active Galactic Nuclei, galaxies, quasars, and discordant (non Hubble flow)
redshifts. [Added 28 October 2003.]
* * *
Figure 5 shows a "Milky Way" Cosmos. In 5a a density profile line is shown piercing a globular cluster, a spiral nebula, and the Milky Way galactic disk. A density plot, along the profile line, is shown in 5b. The Solar System is located near the peak for the galactic disk.
Material Density as a function of Galactic Location
A Note of Caution About Using Cepheid Variables as Standard Candles
[Added 23 January 2004.]
According to the author's EAS model of physics,
not only is the unit electrical charge an environmenally determined
variable, but so is the gravitational constant (G). (In the EAS
model gravity is a shielding side effect of elementary electrical
In this article Cepheid variables are being portrayed as Ritzian
objects, i.e., binary stars where c+v effects (with respect to us
as remote observers) produce periodic brightness variations. (See:
A Ritzian Interpretation of Variable Stars and
Non-Pulsating Cepheid Variables.)
What the above two paragraphs are leading to, is the idea that using
Cepheid variables as standard candles for galactic versus so-called
extra-galactic environments may not be what it's cracked up
to be. For Ritzian Cepheids, which happen to be located in or near the
equatorial part of the galactic disk (where the gravitational constant G
may be considered as more or less normal), we observe Type I
(first studied) Cepheids. For Cepheids located on the fringes of the
galactic disk, or further out into the galactic halo we should expect to
see, kilogram-for-kilogram, longer periods giving us a transition
to Type II Cepheids and perhaps beyond. [This needs more work.]
The following, overly simplified, diagram is meant to illustrate the
postulated interplay between G and the periods of Cepheids as binary stars.
(For circular orbits the separation between the stars will be a constant
R + r.)
It may be that the lengths of the orbital radii R and r will
also be functions of G.
Van Maanen's local spirals may make a comeback. If so, they will be
relatively small (planetary-nebula-like in some cases) near by
members of the Milky Way structure, probably located just outside the
outer-most layer of the disk. Their internal motions will be found to
not be principally subject to Keplerian dynamics but most their
behavior will likely be in accordance with the conventions of plasma and
(GJ2), (ionized gaseous matter moving en-masse; sweeping electrically charged stars
along in the stream.) - Refs added 06 August 2003. - (GJ2) link no longer works.]
If the spirals are clustered near the galactic plane then there is no
requirement for missing mass to make them behave the way we want
them to. We should learn to accept their behavior as it is, and adjust our
theoretical outlooks so as to conform to the way the universe is.
Cosmological redshift may turn out to not be a measure of an
expanding universe. If so, according to the variable electric charge model,
it can be used as a measure of density differences between our observing
vantage point and the remote objects observed. Galaxy clusters should at
least become short, stubby fingers of God.
AH98 - Arp, Halton C.,
Seeing Red: Redshifts, Cosmology and Academic Science, Apeiron, Montreal, pp. 20, 42, 208, 214 (1988). (Part 6)
AR79 - Annual Reviews - Astron. Astrophys, 17, 135-187 (1979)
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BA02 - Bell, Andrew - Wavelengths - Nineteenth-Century Spectroscopy
and the birth of Modern Astrophysics (Part II) -
Link was http://nchalada.org/archive/WaveLng21.html (Part 4)
BBCN - BBC News - Dead stars could be 'missing mass' - 22 March 2001
http://news.bbc.co.uk/1/hi/sci/tech/1236460.stm (Part 1)
BR03 - Britt, Robert Roy, "Hubble Pictures Too Crisp, Challenging Theories of Time and Space,"
Falun Dafa - Minghui.org (Originally was Space.com/science/astronomy, 02 April 2003,)
http://en.minghui.org/emh/articles/2003/4/8/34268.html (Part 2)
[Added 24 March 2004. - Updated 02 Aug 2016.]
BSVD - van den Bergh, Sidney, Dark Matter in the Local Group,
[Link no longer works - 20 Jan 2012] (Part 1)
CE01 - The Columbia Encyclopedia, Sixth Edition, (2001)
Link was http://www.bartleby.com/65/pr/propermo.html (Part 3, Table 3)
CXO - Chandra X-Ray Observatory - Dark Matter Mystery
http://chandra.harvard.edu/xray_astro/dark_matter.html (Part 1)
DJ - Dursi, Jonathan, Cosmology is the study of the evolution of the Universe
Link was www.astro.queensu.ca
- (Parts 1, 5)
DL - Desroches, Louis, Redshift-space distortions
http://astron.berkeley.edu/~louis/astro228/redshift.html (Part 5)
DMVM - Dark Matter vs MOND
http://www.astro.umd.edu/~ssm/mond/mondvsDM.html (Part 1)
DP00 - Durrell, Patrick R., Ciardullo, Robin, Laychak, Marry Beth, Jacoby,
George H., Feldmeier, John J., and Moody, Ken, Kinematics of M33's Disc
Planetary Nebulae - Figure 4: The 'smoothed' rotation curve derived from the
PNe velocities compared to the HI curve from Corbelli & Salucci, (2000).
(Curves very similar.) Radial velocities obtained for 142 planetary nebulae.
http://www.astro.psu.edu/users/pdurrell/M33_aas_poster.pdf (Part 3, Table 2)
See Ciardullo, Robin, et al,
The Planetary Nebula System of M33 (2008)
DT71 - Dixon, Robert T., Dynamic Astronomy, Prentice Hall, Inc.
Englewood Cliffs, NJ, (1971). (Part 3)
FR88 - Fritzius, Robert, Cosmological Redshift, Magnolia Scientific Tech
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http://www.datasync.com../cosmo_rs.htm (Part 6)
FR93 - Fritzius, Robert, Emission-Absorption-Scattering (EAS) Sub-quantum Physics,
Presented at the International Conference on Sir Isaac Newton, St. Petersburg, Russia,
22-27 March, (1993)
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GJ -Goodman, Jason - The Case Against the Big Bang
http://www.geocities.com/kingvegeta80/BBT.html (Part 5) - Link no longer works.
GJ2 - Goodman, Jason - The Case for Plasma Cosmology
Was at: http://www.geocities.com/kingvegeta80/plasma.html (Part 6) - Link no longer works.
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Quarterly Journal of the Royal Astronomical Society, 10, 293-307 (1969).
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HB92 - Hetherington, N., Brashear, R., Journal for the History of Astronomy, 23, 53-56 (1992).
HE35 - Hubble, Edwin, ApJ, 81, 334-335 (1935).
NADS (Part 5)
HE38 - Hubble, Edwin, ASPL, 3, 120-123 (1983).
NADS (Part 6) -
[Added 24 January 2004.]
HM31 - Humason, Milton L., Apparent Velocity-Shifts in the Spectra of Faint Nebulae, ApJ 74, 35-42 (1931) -
NADS (Part 5) -
[Added 25 October 2003.]
HM97 - Hoskin, Michael, The Cambridge Illustrated History of Astronomy,, Cambridge University Press, (1997), page 333. (Part 5)
HPA - History of Leander McCormick Observatory - Hall of Precision Astrometry -
Measuring Engines and Blink Comparators - Gaertner Single Screw Measuring Engine, (1916)
http://www.astro.virginia.edu/~afs5z/gaertner1.html (Part 4)
IPRV - Ivanchik, A., Petitjean, P., Rodriguez, E., and Varshalovich, D.,
Does the proton-to-electron mass ratio mu = Mp/Me vary in the course of cosmological evolution? -
arXiv:astro-ph/0210299 v1, 14 Oct (2002) -
http://arxiv.org/PS_cache/astro-ph/pdf/0210/0210299v1.pdf" (Part 6)
[Added 07 Aug 2003.]
IU - "Island Universes"/ Galaxies: Conflict and Resolution
http://physics.syr.edu/courses/AST104.99Spring/Island.htm (Parts 4, 5)
KA00 - King, Ivan R., and Anderson, Jay, Internal Motions in Globular Clusters, Dynamics of
Star Clusters and the Milky Way ASP Conference Series, Vol. 000, (2000), Deiters, Fuchs, Spurzem
and Wielen, eds.
http://arxiv.org/PS_cache/astro-ph/pdf/0007/0007028.pdf (Part 4)
KW03 - Keel, William, Alternate Approaches and the Redshift Controversy -
http://astr.ua.edu/keel/galaxies/arp/html (Part 6) -
[Added 28 Oct 2003]
LB27 -Lindblad, Bertil, On the Nature of the Spiral Nebulae, MNRAS, 87, 420-426 (1927). -
LJ99 - Lucey, John, Distance to the Hyades via Moving-Cluster Parallax -
http://www.dur.ac.uk/john.lucey/astrolab/hyades_cp.html (Part 3, Table 3)
LK26 - Lundmark K, Internal Motions of Messier 33, Ap.J., 63, 67 (1926). -
(Part 5) [Added 05 October 2003.]
MA21 - Maanen, Adriaan van - "Investigations on Proper Motion - Fifth Paper: The Internal Motion
in the Spiral Nebula Messier 81" Ap.J., 54, 347-356 (1921).
(Parts 3, 4)
MA23 - Maanen, Adriaan van - "Investigations on Proper Motion - Tenth Paper: Internal Motion
in the Spiral Nebula Messier 33, N.G.C. 598" - Ap.J., 57,
264 (1923). -
(Part 3) [Added 7 July 2005.]
MA27 - Maanen, Adriaan van, - Investigations on Proper Motion - Twelfth Paper: The Proper Motions
and Internal Motions of Messier 2, 13, and 56. Ap.J., 66, 89-112 (1927). -
(Parts 3, 4)
MA30 - Maanen, Adriaan van, - Investigations on Proper Motion - Sixteenth
Paper: The Proper Motion of Messier 51, MGC 5194. Contributions from
the Mount Wilson Solar Observatory, 408,
MA35 - Maanen, Adriaan van, ApJ, 81, 336-337 (1935).
NADS (Part 5)
MD&SP - Méndez, Bryan and Seitzer, Patrick, Precision CCD Astrometry,
http://cse.ssl.berkeley.edu/bmendez/html/figures.html (Part 5)
MS1 - McGaugh, Stacy, The MOND pages
http://www.astro.umd.edu/~ssm/mond/mondvsDM.html (Part 2)
MS2 - McGaugh, Stacy - Dwarf and Low Surface Brightness Galaxies
http://xxx.lanl.gov/abs/astro-ph/9507058 (Part 2)
MW02 - Mathis, H. and White, S.D.M., "Numerical simulations of Peebles's Isocurvature Cold Dark Matter
http://www.mpa-garching.mpg.de/~virgo/virgo/hmathis/ICDM (Part 2) [Added 11 March 2004.]
ND80 - Narlikar, J.V., and Das, P.K., Anomalous Redshifts of Quasi-Stellar Objects,
ApJ 240, 401-414 (1980). -
NADS (Part 6)
NF03 - Nicastro, Fabrizio, et al - Missing Mass Exists as Warm Intergalactic Fog, (2003)
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NN02 - Noriaki Namba - Stellar Movement in the Galaxy Explained by Inertial Induction, (2002)
15, 156-161. (Part 2) [Added 20 April 2004.]
NNR02 - NASA News Release - Chandra casts cloud on alternative to dark matter, (2002)
http://www1.msfc.nasa.gov/NEWSROOM/news/releases/2002/02-264.html (Part 2)
This article is probably archived. Haven't located it yet.
NRV - Nieuwenhove, Rudi van, Is the missing mass really missing?
NV02 - Narlikar, J.V., Vishwakarma, R.G., Banerjee, S.K., Das, P.K., Arp, H.C., Dynamics of Ejection
From Galaxies and the Variable Mass Hypothesis, International Journal of Modern Physics D,
11, 245-257 (2002) -
World Science Abstract
PA88 - Peratt, A. "Hannes Alfvén (1908-1995)" - The World and I, pp.190-197, (1988).
http://public.lanl.gov/alp/plasma/people/alfven.html (Part 6)
- [Added 06 August 2003.] - Thanks to John Fritzius of Arnold Missouri for the link.
PICDM-1 - Peebles, P. J. E. "An Isocurvature Cold Dark Matter Cosmonogy. I A Worked Example of
Evolution Through Inflation" -
ApJ 510, 523-530 (1999). -
PICDM-2 - Peebles, P. J. E., "An Isocurvature Cold Dark Matter Cosmonogy. II Observational Tests" -
ApJ 510, 531-540 (1999). -
RW08 - Ritz, Walter, Recherches critiques sur l'Électrodynamique Générale,
Annales de Chimie et de Physique, 13, 145-278 (1908). English translation online at:
http://www.datasync.com../crit/1908a.htm (Part 2)
SC21 - Harlow Shapley & Heber D. Curtis - The Scale of the Universe,
NRC Transcripts of the "Great Debate"
Bulletin of the National Research Council,
Volume 2, Part 3, Number 11, pp 171-217 (May 1921).
http://antwrp.gsfc.nasa.gov/diamond_jubilee/1920/cs_nrc.html (Parts 2, 3)
SEV94 - Savage, D., Elliot, J., and Villard, R. -
Hubble Rules Out a Leading Explanation For Dark Matter" - NASA Release
94-188 (Part 1)
SMKU - Seishi Matsuki, Kyoto University, Dark matter - the mystery of missing mass
Link was http://www.oxford-instruments.com/SCNRMP13.htm - 15 January 2003. (Part 1)
SNP - ScienceNet - Physics - What is the Missing Mass problem?
Was at: http://www.sciencenet.org.uk/database/Physics/Cosmology/p00717c.html (Part 1)
SRR90 - Sharma, Rati Ram, Unified Physical Theory, A Falcon Book from Cosmo Publications,
New Delhi, India (1990). For some recent research that builds on Sharma's 1990 work see
Abridged. (Part 1) [Added 25 March 2004.]
SV87 - Vladimir Sekerin - Gnosiological Peculiarities in the Interpretation
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Contemporary Science and Regularity in its Development, 4,
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TV95 - Trimble, Virginia
The 1920 Shapley-Curtis Discussion: Background, Issues, and Outcome - (Prepared for the 1995 75th
Anniversary Astronomical Debate and for Publications of the Astronomical Society of the Pacific. -
http://antwrp.gsfc.nasa.gov/diamond_jubilee/papers/trimble.html (Part 4)
Related Webpages and Articles
The Mystery of the Missing Mass - History.NASA,gov -
The problem of the missing mass has gotten to the point where it is more than just a problem. It is an
embarrassment, an obstacle to understanding such things as the structure of galaxies, the evolution of
clusters of galaxies, and the ultimate fate of the universe. [Added 20-Dec 2017.]
Cosmology looks beyond the standard model - Astronomy Magazine - Tuesday July 7, 2015
[Added 02 DEC 2015.]
Clouds gather over 'dark matter' - Astronomers challenge assumptions on
galaxies' formation - Keay Davidson, San Francisco Chronicle - Monday
September 8, 2003. [Added 30 November 2004.]
fractaluniverse.org - Colin Hill -
Photographic Evidence of plasma dynamics overpowering gravity in astronomical objects.
[Added 9 May 2004.]