Question

Earth is about 150 million kilometers from the Sun, and the apparent brightness of the Sun in our sky is about 1300 watts/m2. Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at the following positions. 10 times earth's distance from the sun in watts/m^2

Answer 1

`13 W/m^2`

Step-by-step explanation:

The apparent brightness follows an inverse square law, therefore we can write:

`I \propto (1)/(r^2)`

where I is the apparent brightness and r is the distance from the Sun.

We can also rewrite the law as

`(I_2)/(I_1)=(r_1^2)/(r_2^2)` (1)

where in this problem, we have:

`I_1 = 1300 W/m^2` apparent brightness at a distance
`r_1`, where

`r_1 = 150` million km

We want to estimate the apparent brightness at
`r_2`, where
`r_2` is ten times
`r_1`, so

`r_2 = 10 r_1`

Re-arranging eq.(1), we find
`I_2`:

`I_2 = (r_1^2)/(r_2^2)I_1 = (r_1^2)/((10r_1)^2)(1300)=(1)/(100)(1300)=13 W/m^2`