Re: how does dark matter allow a galaxy to have a constant rotation?

Both dark matter and ordinary matter create the gravitational field in the Milky Way and other galaxies. Astronomers can trace the distribution of this matter in a galaxy by determination of the speeds of orbits as a function of distance from the center of the galaxy.

By "constant rotation," we mean that the orbital speeds are (nearly) the same for stars at any distance from the galaxy center. Our Sun, for example, orbits in the Milky Way at a speed of about 220 kilometers per second. Stars that are closer in or further out orbit at about the same speed. Note that stars located toward the galactic center are in orbits that are smaller in size, so they will complete an orbit in less time than does the Sun. Similarly, stars on larger orbits take longer (in years) to orbit.

These orbital speeds are very different from the situation in the Solar System. There, the various planets orbit at different speeds: the ones close in (Mercury, Venus) have much faster speeds than the ones further out (Uranus or Neptune). The farther out a planet is, the slower its speed in its orbit. This happens because practically all the mass in the Solar System is in the center: the Sun has 99.99% of the mass of the Solar System.

The stars in the Milky Way and other galaxies have speeds which are constant with orbital size because the mass in the galaxy is not all concentrated in the center. The central region is the densest part, but a non-negligible fraction of the mass is distributed well away from the center. The mass is distributed in such a way that the orbital speeds are nearly the same with distance from the center.

Astronomers were really surprised when this was discovered, because the light of a galaxy is strongly concentrated toward the center. If stars made up all the mass, then we should expect a situation like our Solar System, in which the speeds decrease the further away the stars are. This showed that something besides stars was also making the gravity, and that this something (whatever it is) is less centrally concentrated - or more widely dispersed - than are the stars. Furthermore, if one adds up the mass known to be in stars, the Sun should be orbiting the galaxy at a speed more like 150 kilometers per second. That shows that this gravity-producing stuff contains more mass than does the stars. Since this stuff does not itself emit light, we call it dark matter. The nature of dark matter is mostly unknown.