Astronomers use a technique called stellar stereography todetermine the density of stars in a star cluster from theobserved (two-dimensional) density that can be analyzedfrom a photograph. Suppose that in a spherical cluster ofradius R the density of stars depends only on the distancefrom the center of the cluster. If the perceived star density isgiven by y(s) , where is the observed planar distance fromthe center of the cluster, and x (r ) is the actual density, it canbe shown that y(s) = integral s to r 2 r /sqrt ( r2 - s2 ) 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)

Astronomers use a technique called stellar stereography todetermine the density of stars in a star cluster from theobserved (two-dimensional) density that can be analyzedfrom a photograph. Suppose that in a spherical cluster ofradius R the density of stars depends only on the distancefrom the center of the cluster. If the perceived star density isgiven by y(s) , where is the observed planar distance fromthe center of the cluster, and x (r ) is the actual density, it canbe shown that y(s) = integral s to r 2 r /sqrt ( r2 - s2 ) 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)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 45E

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