Скачать или смотреть Astronomers use a technique called stellar stereography to determine the density of stars in a star…

Astronomers use a technique called stellar stereography to determine the density of stars in a star cluster from the observed (two-dimensional) density that can be analyzed from a photograph. Suppose that in a spherical cluster of radius R the density of stars depends only on the distance r from the center of the cluster. If the perceived star density is given by y(s) , where s is the observed planar distance from the center of the cluster, and x(r) is the actual density, it can be shown that y(s) = ∫_s^R 2r/√(r^2 - s^2) x(r) dr If the actual density of stars in a cluster is x(r) = 1/2 (R - r)^2 , find the perceived density y(s) .

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