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

various parts have been answered

Step-by-step explanation:

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

initial distance from sun to earth is
`r_1=150*10^6`

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=(150*10^6)/(2)`

then apparent brightness is
`I_2=(I_1r_1^2)/(r_2^2)=(1300* 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=(I_1r_1^2)/(r_2^2)=(1300* 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=(I_1r_1^2)/(r_2^2)=(1300* r_1^2)/((7r_1)^2)=26.5\,W/m^2`