$8.$ A particular star is $=44\mathrm{.}1()$ away, with a power output of $=3\mathrm{.}601026.$ Note that one light$-$year is the distance traveled by the light through a vacuum in one year. a$)$ Calculate the intensity of the emitted light at distance $($in $/2).$ b$)$ What is the power of the emitted light intercepted by the Earth $($in $)?($The radius of Earth is $6\mathrm{.}37106.)$ What If$?$ Of the more than $150$ stars within $20$ of Earth, $90$ are very dim red dwarf stars each with an average luminosity of $2\mathrm{.}001025,$ about $5\%$ the luminosity of the Sun. If the average distance of these objects from the Earth is $10\mathrm{.}0,$ find the following. c$)$ the ratio of the total intensity of starlight from these $90$ stars to the intensity of the single bright star found in part $($a$).$ d$)$ the ratio of the total power the Earth intercepts from these stars to the power intercepted from the bright star in part $($b$).$