Question

The intensity of sunlight at the Earth is about 1367 W/m^2. How many times further away would the Sun have to be from the Earth before solar radiation was only as intense as a 100W light bulb 10 meters away, assuming that all energy from the bulb goes into radiation and spreads out evenly in all directions?

Answer 1

The intensity of sunlight on the Earth is about 1367 W/m^2. The earth has to be 131 the distance farther away

This is further explained below.

What is the distance?

Generally, bet the power emitted by the sun is P. so. at the distance of earth intensely where $r_E$ is the distance of the earth from the sun. were $I_1=1362 \frac{w}{m^2}$

Therefore

p=4 $\pi 1367 r_E^2$

let at distance $\gamma r_E$ is a positive number) the intensity is the same as the intensity at 10m away from a 100w bulb. So.

In conclusion,

$\begin{aligned}&\frac{P}{4 \pi\left(\gamma r_{\varepsilon}\right)^2}=\frac{100}{4 \pi 10^2}\\\\&\text { or, }\left(\gamma r_E\right)^2=P=4 \pi 1367 r_E^2\\\\&\therefore \gamma=\sqrt{4 \pi \times 1367}\\\\&=131.06\\\\ }\end{aligned}$

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