The Globular Cluster M13 Is a Spherical Distribution of Stars $\rho(r)=\left(1+\left(\frac{r}{90}\right)^{3}\right)^{-5}$

question 43

Short Answer

The globular cluster M13 is a spherical distribution of stars which orbits our galaxy.Suppose that the density of stars in the cluster is purely a function of distance r from the center of the cluster and is given as $\rho(r)=\left(1+\left(\frac{r}{90}\right)^{3}\right)^{-5}$ stars/(ly)³, where r is measured in light-years, and 0 $\le$ r $\le$ 90 ly.(One light-year is the distance light travels in one year; "light-year" is abbreviated as "ly".)Find the number of stars in M13.Round to the nearest whole number.

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