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.

Answer 1

The question is incomplete. Here is the complete one.

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: A) Half Earth's distance from the Sun; B) Twice Earth's distance form the Sun; C) 7 times Earth's distance from the Sun;

Answer: A) 5200 W/m²; B) 352 W/m²; C) 26.53 W/m²;

Explanation: A point source that spreads its influence in all directions follows the Inverse Square Law. It states the intensity of the source at any given radius r is the source's strength divided by the area of a sphere. It basically shows that if the radius r doubles, the intensity I is 1/4 of the intensity. So,

A) The apparent brightness of the Sun is 1300W/m² and Earth is 150 million km from the Sun. To find the brightness at half Earth's distance, we have to compare each other, which mean:

$\frac{I_{T} }{I_{1/2} } = (\frac{r_{2} }{r_{1} })^{2}$

$I_{1/2} = I_{T} . (\frac{r_{1} }{r_{2} }) ^{2}$

$I_{1/2} = 1300. (\frac{150}{\frac{150}{2} }) ^{2}$

$I_{1/2} = 1300.2^{2}$

$I_{1/2}$ = 5200 W/m²

B) For twice the Earth's distance:

$I_{2} = I_{T} . (\frac{r_{1} }{r_{2} }) ^{2}$

$I_{2} = 1300 . (\frac{150 }{300 }) ^{2}$

$I_{2} = 1300 . 0.5 ^{2}$

$I_{2} =$ 325 W/m²

C) For 7 times the Earth's distance:

$I_{7} = I_{T} . (\frac{r_{1} }{r_{2} }) ^{2}$

$I_{7} = 1300 . (\frac{150}{7.150}) ^{2}$

$I_{7} = 1300 . (\frac{1}{7} ) ^{2}$

$I_{7} =$ 26.53 W/m²

Answer 2

3) Earth is about 150 million km from the Sun, and the apparent brightness of the Sun in our sky is about 1,300 watts per square meter. Determine the apparent brightness we would measure for the Sun if we were located five times Earth's distance from the Sun. Answer: The Sun would appear 1/25 times as bright.