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A.R. Upgren (Yale and Wesleyan Universities)
Zipf's law is a power law that describes the frequency of occurrence of many events in nature and in human affairs. It has recently found a resonance among some of the natural phenomena in the Earth sciences. Here we extend its applicability to astronomy. The essence of this law is that the sizes of objects or the frequencies of events adhere closely to a linear power law in which P, their frequency or size is a function of its rank; that is, P(i) ~ 1/ia with the exponent, a, lying close to unity for many widely differing phenomena. Thus, i = 1, 2, 3, 4, . . . and P(i) ~ 1, \onehalf, . . . We examine the brightnesses of the naked-eye stars and compare their distribution to city populations and other examples of Zipf's law in other disciplines.
At first glance it would seem that everything about these stars has long been known, but this is far from the case. In their classic 1953 text, Statistical Astronomy, Robert Trumpler and Harold Weaver (along with other authors since) list eight parameters that can define a star rather uniquely, to which we add a ninth. At that time, the only reliably known data for all or almost all of the 9110 BSC stars were their apparent magnitudes and proper motions. Reliable distances and parallaxes were known for few, and accurate radial velocities for almost none. But today photoelectric photometry and radial velocities are known for most, and parallaxes from the recent Hipparcos Catalogue for all. Only the age, through [Fe/H] or other, is not known for many of the stars; we can hope that this will be corrected in years to come.
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Bulletin of the American Astronomical Society, 35#5
© 2003. The American Astronomical Soceity.