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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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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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
from the center of the cluster. If the perceived star density is
given by y(s) , where 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) = 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)

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