 Fast forward to the 1970s, attention was focused on an anomaly associated with the velocity of stars orbiting spiral galaxies. Resolving the velocities of individual stars in distant galaxies is not feasible, but in spiral galaxies where all the stars in the disk are rotating in the same direction, a good aggregate estimate is possible. With elliptical galaxies, the motion of stars around the center are chaotic, so we have no velocity data to use and therefore no anomalies to identify. To see how the velocities give us a measure of mass, we'll start with our solar system. Here's the rotation curve we get when we map the velocity of the planets orbiting the Sun. Because the Sun has 99% of all the matter in the system, the mass within any orbit will be relatively fixed at the Sun's mass. Therefore the further away from the central mass we get, the weaker the gravitational pull and the slower the orbital velocity. This model is called Keplerian because it follows Kepler's laws for orbital motion. Now a galaxy is much more complex than a solar system. The mass within increasing orbital volumes is not fixed like it is in the solar system. If you move out from the center of a galaxy, there is considerable mass added in addition to the mass of the central bulge. This is because of the large number of stars, dust and gas in the galaxy's disk. For instance, it is estimated that the mass of the central bulge of the Milky Way is 20 billion solar masses. We saw in our segment on the Milky Way that the velocity of the Sun around the center of the galaxy is 200 km per second, and its distance from the center is 26,000 light years. So the mass of the galaxy's interior to the Sun's orbit is approximately 74 billion solar masses. A good deal more than the bulge itself. But at the outer edges of the disk, the star density drops off dramatically. In the 1970s everyone expected to see rotation curves that look like this. But in 1975 an American astronomer Vera Rubin published galaxy rotation curves for the Milky Way and a number of other galaxies that showed a remarkable result. Where the velocities were expected to fall off, they remained relatively constant. If our current theory of gravity holds up for galactic distances, then this curve tells us that our model of the Milky Way is missing something. In order for objects far from the center of the galaxy to be moving faster than predicted, there must be significant additional mass far from the galactic center exerting gravitational pulls on those stars. In other words, dark matter. Here's Vera Rubin's measurements of the velocity curve for Andromeda. And here's the rotation curve for NGC 6503, the galaxy on the edge of the local void that we covered earlier. Using accurate and high resolution emission lines from neutral hydrogen, astronomers modeled the mass distribution of this galaxy. They used the mass to light ratio in the visible disk, the galaxy's core radius, and the circular velocity of the halo. The study found the contribution to the rotation curve of three types of matter, gas, luminous matter, and dark matter.