Consider an observer at the center of a uniform, spherical cluster, of radius R, containing many stars. Assume that the density of stars is given by n(r) stars per cm^3
n(r)=n0* (r/r0)^-α
a. Write a formula for the flux arriving at the observer from one of the stars as radius r from the center.
b. Consider a thin shell of stars at radius r, with thickness dr. Estimate the number dN of stars in the shell.
c. Estimate the total radiation flux, from all directions, received by the observer from the thin shell of stars in part b.
d.Integrate over all of the shells to calculate the total flux received by the observer form all directions, form the entire cluster, which extends to infinity. (note that you should consider all cases, including a special case that leads to a logarithm when you integrate, not a power law.)
e. Which values of α lead to finite/infinite flux at the cluster center?