Estimate the distance of a fading white dwarf supernova of luminosity 108lsun whose apparent brightness is comparable to that of a bright cepheid variable star 100 million light-years from earth.

The supernova is a fraction of 0.7 of the size of the observable universe which is 10 billion light years away.

Explanation:

Apparent brightness(AB) = luminosity(L) / 4πr²

∴ Luminosity(L) = Apparent brightness(AB) × 4πr²

Ratio of the luminosity of cepheid and supernova with the same brightness will be written as;

Therefore,    ...................(a)

Since we already have as 100 million light year, substitute for luminosity of supernova and luminosity of cepheid as 10⁸ and 10,000 respectively in equation (a)

==> 10 billion light year

the ratio of the distance to the size of the universe:

Supernova / Observable Universe  = (10 / 14) billion light years

Supernova / Observable Universe  = 0.7