determining distance using luminosity

I have a question where I am asked to determine the apparent distance in light years using brightness and luminosity: With a very large telescope on a very dark night we can detect a star like our Sun that appears just 10^−20× as bright as our Sun does during the day. Use this information to determine how far that very faint sun is from Earth.

The answer choices are: (A) 1600 ly, (B) 6000 ly, (C) 16,000 ly, (D) 60,000 ly, (E) 160,000 ly

The answer I calculated was closest to (D), my exact answer that I got is 49,125.553 ly and here is how I got that:

Using the formula d^2 = L / 4*pi*B
Where L = luminosity in watts, B = apparent brightness and d^2 is the distance in meters

so the question said bright as the Sun, so I used the Sun’s luminosity which is 3.8 x 10^26 Watts
and for brightness B, I calculated it using the apparent brightness of the Sun, which I searched was 1.4 × 10^3 W/m^2 and then multiplied it by 10^-20, because the question said that the brightness of the star we are looking at has a brightness of 10^-20 x brightness of the Sun.

So then I plugged in those values and ended up with an answer in meters and converted to light years and got approx. 50,000 ly.

That’s my shot at the answer, but I still don’t fully understand how I did this question.

Leave a Reply

Name *
Email *