Galaxy rotation problemspiral galaxies and the predictions of Newtonian dynamics considering the luminous mass. Attempts to resolve the galaxy rotation problem have included the hypothesis of dark matter and the hypothesis known as Modified Newtonian Dynamics.
In the beginning of the 1980s, the first observational evidence was reported that spiral galaxies do not spin as expected according to then current theories. A typical spiral consists of a large central bulge surrounding by a thin disk. Orbits of stars in the disk portion typically have low eccentricities and thus can be approximated to first order by circles.
Based on this model, matter (such as stars and gas) in the disk portion of a spiral should revolve around the center of the galaxy with orbits that are nearly Keplerian. That is, according to Newtonian mechanics, the orbit should approximate that of an object in a two-body gravitational system in which all the matter inside the radius of the orbit is concentrated in a point at the center of the galaxy, like a two-body planetary system. Outside of local perturbations, matter outside the radius of the orbit does not affect the characteristics of the orbit.
As a result, based on Newton's laws, it would be expected that the average orbital speed of an object in rotation at a given radius would decrease inversely with the square root of the radius of the orbit (the dashed line in Fig. 1).
Observations of the rotation curve of spirals, however, do not bear this out. Rather, the curves do not decrease in the expected inverse square root relationship but are "flat." That, outside of the central bulge, the speed is nearly a constant function of radius (the solid line Fig. 1). Astronomers call this phenomenon the "flattening of galaxies' rotation curve."
The cause of the flattening of rotation curves of spirals is still an open question. The most popular hypothesis the phenonenon is the result of the presence of dark matter within the galactic halo. Dark matter also appears in current cosmological theories. Dark matter has, however, not been observed so far.
Another explanation that has been offered is the Modified Newtonian Dynamics (MOND) theory.