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

The correct answer is option 'c': 30 AUs

Step-by-step 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=(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'=(e_(1))/(900)\\\\(E)/(4\pi r_(2)^(2))=(1)/(900)* (E)/(4\pi r_(1)^(2))\\\\\Rightarrow r_(2)^(2)={r_(1)^(2)}* 900\\\\\therefore r_(2)={r_(1)}* {30}`

Thus the distance increases 30 times.