A particular star is d$=80\mathrm{.}1$ light$-$years $($ly$)$ away, with a power output of P$=3\mathrm{.}20\backslash$times $10^(26)$W$.$ 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 dn$($W$)/($m$^(2))$ n$($W$)/($m$^(2))6\mathrm{.}37\backslash$times $10^(6)$m$\mathrm{.}2\mathrm{.}00\backslash$times $10^(25)$ W$,$ about $5\%$ the

luminosity of the Sun. If the average distance of these objects from the Earth is $10\mathrm{.}0$ ly $,$ 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$)$

$($I$\_($dwarf stars $))/($I$\_($single star $))=$

$($d$)$ the ratio of the total power the Earth intercepts from these stars to the power intercepted from the bright star in part $($b$)$

$($P$\_($dwarf stars $))/($P$\_($single star $))=$