thousands to tens of thousands of miles. Stars come next, with radii ranging from hundreds of thousands to tens of millions of miles. (Note that such gargantuan figures represent living stars; extinguished ones, such as white dwarfs, neutron stars, and black holes are much smaller.) Systems in the fourth class, stellar clusters, have sizes best expressed in terms of light-years. Typically, they are on the order of 10 light-years across. (Recall that a light-year is approximately 6 trillion miles.)

Now let’s take a colossal leap and turn to the fifth category— galaxies. These objects are ordinarily hundreds of thousands of light-years across. Clusters of galaxies, the sixth rung on this astronomical ladder, generally contain between 50 and 1,000 galaxies within a region roughly 10 million light-years across. Finally, the seventh level includes superclusters and even larger structures, such as filaments, bubbles, and walls. Superclusters typically have total populations of as many as 10,000 galaxies, housed in a sector about 100 million light-years across. Astronomers used to think they were the largest structures in the universe, until in the 1980s a team led by Margaret Geller and John Huchra of the Harvard-Smithsonian Center for Astrophysics mapped out a three-dimensional slice of space, revealing vast, spongy arrangements of galaxies. In their cosmic map, stringy, bubbly and sheetlike arrays of galaxies—called filaments, bubbles and walls, respectively—bounded relatively empty regions, called voids. The largest structure they found was the “Great Wall,” a sheet of galaxies stretching out more than half a billion light-years across.

If nature’s operating principle is self-similarity, it behooves us to search for commonalities on all scales. One natural place to look is in the density distribution of various astronomical structures, which indicates how much of their material lies at their centers and how much is peripheral. Clearly, because these systems have mass, the inverse-square law of gravitation constitutes one part of the picture. Additionally, because many of these systems are rotating, their total



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