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

Answer:

316227.766 kpc

Explanation:

Brightness is given by

$B=\dfrac{L}{4\pi d^2}$

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

$\dfrac{L_1}{4\pi d_1^2}=\dfrac{L}{4\pi d^2}\\\Rightarrow d_1=d\sqrt{\dfrac{L_1}{L}}\\\Rightarrow d_1=\sqrt{\dfrac{1\times 10^9L}{L}}\times 10\\\Rightarrow d_1=316227.766\ kpc$

The distance to the galaxy is 316227.766 kpc