The average orbital velocities of planets in the solar system vary as the inverse
square root of distance from the Sun. Thus the Earth orbits at about 30 km/s, Mercury
at 48 km/s and Pluto at a leisurely 4.7 km/s. This behaviour, an expression of Kepler’s
laws of planetary motion, is termed ‘Keplerian’. It arises from Newtonian
dynamics, including the inverse-square law of gravitational attraction, together
with the fact that most of the mass in the solar system is concentrated very close
to the centre in the Sun.
When mid-twentieth century astronomers first investigated galaxy rotations, they
expected orbital velocities outside the nuclear bulge to decrease with distance
from the centre in Keplerian fashion. Indeed the earliest attempts to obtain rotation
curves (plots of orbital velocity against distance from the centre) for spiral galaxies,
although subject to large measurement errors, produced results roughly consistent
with this expectation. However during the 1970s Vera Rubin and colleagues used the
Doppler shifts of spectral lines—mainly optical emission lines from clouds
of ionized hydrogen and the 21-cm radio emission line from neutral hydrogen—to
establish reliable rotation curves for numerous spiral galaxies.1–3 The
results were both surprising and remarkably consistent: rotation curves in the outer
regions of galaxies did not fall with radius in Keplerian fashion. Instead they
stayed roughly constant, or even rose slightly towards the outer edges of galaxies.
An illustrative rotation curve is shown in Figure 1.
The mass discrepancy problem
This result may be viewed as a discrepancy between galaxy masses inferred dynamically
and from their emitted light distributions—the ‘mass discrepancy’
problem. Once generally accepted, it was taken as evidence that galaxies were accompanied
by very significant quantities of otherwise undetected or ‘dark’ matter
distributed up to and often beyond, their visible boundaries.4 This postulated dark matter is important in today’s
mainstream cosmology. Modern cosmology proposes a ‘flat’ inflationary
big-bang universe in which the effective mass density of the universe consists of
dark energy, dark matter and the more familiar visible matter (stars, gas, planets
and the like), with the latter only contributing a few percent of the total. Galaxy
formation is thought to have begun with density variations in the supposed distribution
of dark matter in the early expanding universe. Not only have objects such as white
dwarf stars, brown dwarfs, black holes and neutrinos been proposed to account for
the dark matter, but also various exotic hypothetical objects including gravitinos,
photinos, axions, magnetic monopoles, WIMPs and MACHOs.5
But, we ask, is all this really good science? To begin with, the presence of dark
matter has recently been called into question in creationist6,7 and
in general astronomical literature.8–11
The recent detection of faint white dwarf stars allegedly belonging to the Milky
Way halo population was hailed as revealing a sample of the elusive dark matter.12 However, these stars more
probably belong to a thick galactic disk population.13
Not only this, but have alternative interpretations of the mass discrepancy problem
been proposed and only rejected after careful investigation? The answer to this
last question proves to be very interesting. As early as 1963 Finzi14 suggested a distance-based modification of gravity
to resolve the mass discrepancy problem for galaxy clusters, but this seems to have
received little attention. Then in 1983 the Israeli physicist Moti Milgrom proposed15 a modification of Newtonian
dynamics, known as MOND, designed to reproduce the observed ‘flat’ galaxy
rotation curves using only observed distributions of visible matter and reasonable
assumptions about mass/light ratios as input data. MOND applies at the very low
accelerations which occur in the outer regions of spiral galaxies and in galaxy
groups; accelerations are higher in the familiar (inner) region of the solar system.
The Newtonian equation for a particle moving under gravity, viz
a = GM / r2
(where a is the radial acceleration, G the universal gravitational constant, M the
attracting mass and r the distance from the centre of mass), becomes
a2 / a0 = GM / r2
where a0 is the critical acceleration level below which MOND applies.16 This can be viewed as either
a modification of the law of inertia or of the law of gravity,15 the
latter being preferred because it involves a less radical modification of recognised
physics.17 Indeed there
are still several mysteries surrounding gravity, for example possible shielding
of the Sun’s gravity by the Moon during solar eclipses18,19
and general relativistic ‘frame dragging’, shortly to be investigated
by the Gravity Probe B experiment.20
Van Flandern21 has reviewed
some of the questionable aspects of our understanding of gravity.
Wright, Disney and Thompson22
have suggested a modified (inverse linear) law of gravity beyond a certain distance
scale to explain the mass discrepancy problem in galaxies, galaxy clusters and superclusters.
Liboff23 and others
have considered similar possibilities too, but McGaugh and de Blok24 insist that acceleration, not
distance, is the decisive factor. This is because the mass discrepancy is less severe
for high surface brightness (HSB) galaxies than for smaller, low surface brightness
(LSB) galaxies where centripetal accelerations fall to extremely low values of order
By using MOND for a single universal value of a0 , i.e. 1.2 ×10–10
ms–2 (about 100 billion times smaller than the acceleration due
to gravity at the Earth’s surface), the rotation curves of many galaxies can
be reproduced without assuming the presence of appreciable quantities of dark matter!25
Testing MOND predictions
When Milgrom’s ideas were first published, sufficient rotation curves of HSB
galaxies were already established that MOND calculations could scarcely be regarded
as predictions; they could rather be viewed as parameter-fitting exercises for a0.
Since then, however, rotation curves for LSB galaxies have become available which
provide a more stringent test of MOND than the earlier data. The results are remarkably
MOND naturally predicts the Tully-Fisher relation for spiral galaxies,27 the observed correlation between rotation velocities
and mass (originally expressed in terms of neutral hydrogen line widths and absolute
luminosity) which is often used as a distance indicator. A detailed comparison between
MOND and ‘Dark Matter’ predictions for a sample of spiral galaxies with
accurately measured rotation curves28
concluded that MOND provided the best available description. This was despite ‘Dark
Matter’ being allowed three adjustable model parameters, while in most cases
MOND was only allowed one, the mass/light ratio for each galaxy. Figure 2 shows
sample MOND fits to measured rotation curves from this paper.
Galaxy rotation is not the only way of testing theories of gravity or inertia. Astronomer
Stacy McGaugh (University of Maryland) has set up a MOND web site,29 which includes a page30 listing itemized comparisons of the predictions
of MOND and ‘Dark Matter’. These deal with the dynamics of individual
elliptical and spiral galaxies of various sizes, motion within galaxy clusters,
large scale structure in the universe, gravitational lensing and indeed the spatial
structure of the cosmic microwave background radiation. Frequently MOND gives clear
predictions where the dark matter hypothesis either has serious fine-tuning problems
or gives no prediction. In most cases MOND predictions match the data very well,
though sometimes the data is inadequate to provide a clear test. Rubin31 briefly alludes to X-ray observations32,33
which apparently discredit MOND predictions for galaxy clusters. However McGaugh
and de Blok24 point out that this data is subject to major uncertainties
which preclude a critical test, and that the dark matter interpretation is also
problematical, and Sanders34
has shown how MOND neatly predicts the mass-temperature relationship for gas-rich
galaxy clusters. Some authors15,17,35
have noted that the MOND acceleration constant a0 is of the same order
as cH0 , where c is the speed of light and H0 the Hubble constant,
thus hinting at its possible cosmological significance.
Gravitational lensing appears to be the least promising area for MOND. However,
this is essentially a GR (general relativistic) phenomenon, and MOND has yet to
be formulated in GR terms. Thus Binney36
has commented that MOND cannot fairly be tested against such effects. Milgrom35
has recently considered its possible origin in vacuum effects, and Sanders37 has shown how scalar-tensor
theories can be constructed which reproduce many MOND predictions. The main objection
to MOND is thus summed up by Livio: ‘Milgrom’s conjecture has not gained
many supporters, primarily because it has never been developed into a truly complete
developments could change this.
Why is MOND unpopular?
The answer to our question regarding the interpretation of the mass discrepancy
problem is, therefore, that MOND is a very successful, albeit purely phenomenological,
alternative to dark matter. It is strongly favoured by Occam’s razor in that
it makes clear predictions and is therefore falsifiable, but remains unfalsified.
However, rather than being carefully investigated by experts in the field, it has
largely been ignored. Those who have commented tend to dismiss it summarily. Thus
Rubin says: ‘this possibility must remain as a last resort’39 and ‘Most astronomers prefer to accept a
universe filled with dark matter rather than to alter Newtonian gravitational theory.’40 Thus it seems that MOND
has been ignored not for objective scientific reasons but largely because it implies
the existence of much less dark matter than is required by the currently dominant
flat, accelerating-universe cosmology which Livio5 regards as so beautiful
that it ‘has’ to be true.
What interest do creationists have in MOND, a purely mechanistic theory, which was
not developed with origins in mind? First, creationist astronomers and cosmologists
should be aware of developments which, at least indirectly, impinge on our understanding
of the astronomical data relevant to creation. Moreover the remarkably successful
predictions of MOND could be pointing to the need for fundamentally new physics
at a time when we are hearing that human understanding of the physical universe
is nearly complete! MOND exposes deep cracks behind the self-confident façade
of modern uniformitarian cosmology and thus reminds us of the fallibility of scientific
paradigms, especially when they have been developed in ignorance of the Creator.
Recall Isaiah 29:14, which says of those who ignore God: ‘
… the wisdom of the wise will perish, the intelligence of the intelligent
Rubin, V.C., Bright Galaxies Dark Matters, Springer-Verlag
Inc., New York, 1996. Return to text.
Rubin, V.C., Ford, W.K., Jr. and Thonnard, N., Rotational
properties of 21 Sc galaxies with a large range of luminosities and radii, from
NCG 4605 (R = 4 kpc) to UGC 2885 (R = 122 kpc), Ap. J. 238:471–487,
1980. Return to text.
Rubin, V.C., Burstein, D., Ford, W.K., Jr. and Thonnard, N.,
Rotation velocities of 16 Sa galaxies and a comparison of Sa, Sb, and Sc rotation
properties, Ap. J.289:81–104, 1985.
Return to text.
Dark matter had also been inferred from the large velocity
dispersions observed in galaxy clusters by Zwicky and Oort in the 1930s.
Return to text.
Livio, M., The Accelerating Universe, John Wiley
& Sons, Inc., New York, 2000. Return to text.
Lucentini, J.A., Handle on dark matter? Sky and Telescope
103(1):16–17, (News Notes, January 2002), 2002.
Return to text.
Olling, R.P. and Merrifield, M.R., Luminous and dark matter
in the Milky Way, MNRAS326(1):164–180, 2001. Return to text.
Binney, J.J. and Evans, N.W., Cuspy dark matter haloes and
the galaxy, MNRAS 327(2), pp. L27–L31, 2001.
Return to text.
Governato, F., Moore, B., Cen, R., Stadel, J., Lake, G. and
Quinn, T., The Local Group as a Test of cosmological models, New Astronomy 2(2):91–106, 1997. Return to text.
Oppenheimer, B.R., Hambly, N.C., Digby, A.P., Hodgkin, S.T.
and Saumon, D., Direct detection of galactic halo dark matter, Science 292(5517):698–702, 2001. Return to text.
Reid, I.N., Sahu, K.C. and Hawley, S.L., High-velocity white
dwarfs: thick disk, not dark matter, Ap. J. 559(2):942–947,
2001. Return to text.
Finzi, A., On the validity of Newton’s Law at a long
distance, MNRAS 127:21–30, 1963.
Return to text.
Milgrom, M., A modification of the Newtonian dynamics as
a possible alternative to the hidden mass hypothesis, Ap. J. 270:365–370,
A modification of the Newtonian dynamics: implications for galaxies, 371–383
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There is a ‘transition range’ of accelerations
characterized by a~a0 where an interpolation function, not prescribed
a priori, is required to match the conventional and MOND regimes, but MOND
predictions do not seem to depend critically on the form chosen for this function.
Return to text.
Bertin, G., Dynamics of Galaxies, Cambridge University
Press, 2000. Return to text.
Wang, Q.S., Yang, X.S., Wu, C.Z., Guo, H.G., Liu, H.C. and
Hua, C.C., Precise measurements of gravity variations during a total solar eclipse,
Phys. Rev. D 62:041101, (pp. 1–3), 2000.
Return to text.
Unnikrishnan, C.S., Mohapatra, A.K. and Gillies, G.T., Anomalous
gravity data during the 1997 total solar eclipse do not support the hypothesis of
gravitational shielding, Phys. Rev. D 63:062002, (pp.
1–4), 2001. Return to text.
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