SIMPLIFIED SUMMARY:
"While Newton's Laws predict that stellar rotation velocities should decrease with distance from the galactic centre, Rubin and collaborators found instead that they remain almost constant– the rotation curves are said to be "flat". This observation necessitates at least one of the following:
1) There exists in galaxies large quantities of unseen matter which boosts the stars' velocities beyond what would be expected on the basis of the visible mass alone, or
2) Newton's Laws do not apply to galaxies.
*The former leads to the dark matter hypothesis; the latter leads to MOND."
Wikipedia
TECHNICAL ANALYSIS:
"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 
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. 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.
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. 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
As early as 1963 Finzi 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 proposed 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 center of mass), becomes
a2 / a0 = GM / r2
where a0 is the critical acceleration level below which MOND applies. This can be viewed as either a modification of the law of inertia or of the law of gravity, the latter being preferred because it involves a less radical modification of recognized physics. Indeed there are still several mysteries s
Wright, Disney and Thompson 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. Liboff and others have considered similar possibilities too, but McGaugh and de Blok 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 10–11 ms–2.
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!
Why is MOND unpopular?
Rubin says: ‘this possibility must remain as a last resort’and ‘Most astronomers prefer to accept a universe filled with dark matter rather than to alter Newtonian gravitational theory.’ 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 Livio regards as so beautiful that it ‘has’ to be true.
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 will vanish.’ CMI