The Earth has a surface temperature around $270$ K and an emissivity of $0\mathrm{.}8,$ while space has a temperature of around $2$ K$.$

Use Stefan's law: P$($net$)=5\mathrm{.}6710-8$ W$/$K$4$ m$2*$A$*$e$*($T$4-$ To$4)$ to solve the following questions.

$($Radii of the Earth and the Sun are Re $=6\mathrm{.}38106$ m$,$ Rs $=7108$ m$.)$

$($a$)$ What is the net power radiated from our Earth into free space in Watt W$?$

P$\_$r $=$ W$$

$($b$)$ If the Earth is in thermal equilibrium, how much power must the Earth absorb from the Sun?

P$\_$abs $=$ W$$

$($c$)$ If the energy absorbed by the Earth from the Sun constitutes only $1/(1010)$ of the Suns total radiant energy to the space, and consider the Sun is a black body, what is the surface temperature of the Sun in Kelvin K$?$

T$\_$sun $=$ K$$