Question

Suppose the Sun appeared to you 900 times dimmer than it does now. How far away from the Sun would you be? (A) 1/9 AU (B) 3 AU (C) 30 AU (D) 90 AUs (E) 900 AUs

Answer 1

Answer:

The correct answer is option 'c': 30 AUs

Explanation:

For a spherical wave front emitted by sun with total energy 'E' the energy density over the surface when it is at a distance 'r' from the sun is given by

$e=\frac{E}{4\pi r^{2}}$

This energy per unit area is sensed by observer as intensity of the sun.

Let the initial intensity of sun at a distance $r_{1}$ be $e_{1}$

Thus if the sun becomes 900 times dimmer we have

$e'=\frac{e_{1}}{900}\\\\\frac{E}{4\pi r_{2}^{2}}=\frac{1}{900}\times \frac{E}{4\pi r_{1}^{2}}\\\\\Rightarrow r_{2}^{2}={r_{1}^{2}}\times 900\\\\\therefore r_{2}={r_{1}}\times {30}$

Thus the distance increases 30 times.