Question

A supernova 1 billion times more luminous than the Sun is used as a standard candle to measure the distance to a faraway galaxy. From Earth, the supernova appears as bright as the Sun would appear from a distance of 10 kpc. Calculate the distance to the galaxy.

Answer 1

316227.766 kpc

Step-by-step explanation:

Brightness is given by

`B=(L)/(4\pi d^2)`

where

L = Luminosity of Sun

d = Distance to the Sun

`d_1` = Distance to the supernova

`L_1` = Luminosity of supernova = 10L

From the above relation we get

`(L_1)/(4\pi d_1^2)=(L)/(4\pi d^2)\\\Rightarrow d_1=d\sqrt{(L_1)/(L)}\\\Rightarrow d_1=\sqrt{(1* 10^9L)/(L)}* 10\\\Rightarrow d_1=316227.766\ kpc`

The distance to the galaxy is 316227.766 kpc