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. Use these two facts and the inverse square law for light to answer the questions.

Answer 1

Answer:

various parts have been answered

Explanation:

Inverse square for light is $I_1r_1^2=I_2r_2^2$

initial distance from sun to earth is$r_1=150\times10^6$

and intensity or apparent brightness of sun is $I_1=1300\ W/m^2$

a)

If distance from sun to earth is $r_2=r_1/2=\frac{150\times10^6}{2}$

then apparent brightness is  $I_2=\frac{I_1r_1^2}{r_2^2}=\frac{1300\times r_1^2}{(r_1/2)^2}=5200$

b)

If distance from sun to earth is  $r_2=2r_1$

then apparent brightness is  $I_2=\frac{I_1r_1^2}{r_2^2}=\frac{1300\times r_1^2}{(2r_1)^2}=325\,W/m^2$

c)

If distance from sun to earth is  $r_2=7r_1$

then apparent brightness is

$I_2=\frac{I_1r_1^2}{r_2^2}=\frac{1300\times r_1^2}{(7r_1)^2}=26.5\,W/m^2$