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Plotting the rotation curve of an individual spiral galaxy—the velocity of disk material versus the distance of that material from the galactic center—yields the mass of the galaxy that lies within that radius. This method gives a good estimate as long as most of a galaxy's mass is contained near its center. In the solar system, for example, the outer planets rotate much more slowly than the inner planets, in accordance with Kepler's Third Law, because the mass of the solar system (99.9 percent of it, anyway) is contained in the sun.

But astronomers soon noticed a problem with galaxies. There are objects in the outer reaches of spiral galaxies (clouds of gas—in particular, clouds of neutral hydrogen called HI clouds) that orbit in a way that indicates that they "see" more mass out there than we do here at the radius of the sun. They are orbiting faster than they should. And using the 21 cm radio line of hydrogen to see the HI, astronomers have traced the rotation curve of many galaxies far beyond the outermost stars. These curves seem to indicate that there is more matter at large radii in these galaxies. Whatever has this mass, though, is something that we can't see, because it is not "shining" at any wavelength. We call it dark matter.

Amazingly, there seems to be about 10 times more matter that we can't see than matter that we can see in most galaxies. And it gets even worse. In clusters of galaxies, the mass-to-light ratio (see Chapter 21) can be 100 or more. That is, luminous matter on very large scales accounts for only 1 percent of the matter that we "see" via gravity.

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