Question

This problem requires putting together several concepts to calculate the tem- perature of the sunlit side of the Moon. The Moon absrorbs most of the sunlight falling on it, reflecting only about 12%. It also rotates about its axis once every 27 days, so it is reasonable to assume one side is much warmer than the other. Assuming an average distance from the Sun of 1 AU and using the solar constant, calculate the temperature of the sunlit side of the Moon.

Answer 1

T=270 K

Step-by-step explanation:

Power absorbed by the Moon

`P_(absorbed)= [1-0.12]solar\ constant*\pi R^2`

the reason for choosing the area as π R^2 and not 4π R^2 is because the absorbed light is only from the surface facing the Sun which is a disc.

Using Stefan Boltzmann's law,

`P_(emitted)= \sigma T^4(4\pi R^2)`

So, using Conservation of Energy,

`[1-0.12]solar\ constant*\pi R^2<strong>=</strong>\sigma T^4(4\pi R^2)`

this gives, T = 270 K. This is the temperature of the sunlight side of the Moon.