Which star has the greater luminosity

[zebra1707]

Homework Statement

Question 1 - If two stars A of luminosity 9000 and B of luminosity 90 (both relative to the Sun) appear equally bright from the Earth, how much further away is A from B?

Question 2 - Star A is twice as bright as Star B, but B is twice as far away as A. Which star has the greater luminosity, and by what ratio?

Question 3 - If two stars, A and B, are the same distance away, but B is 20 times more luminous than A, how much brighter will B appear than A?

I could use some assistance as to how I should set these out in accordance with

brightness (proportional to) Luminosity / R^2

Homework Equations

See above

The Attempt at a Solution

Question 1 - Worked out to - by moving Star A 10 times further away we have diminished the apparent brightness of Star A by a factor 10 x10 = 100 so that it now matches the brightness of Star B.

Question 2 - Worked out to - Luminosity of A
Luminosity of B = (½)2 x 2 = ½

This means that Star A really only has half the luminosity of Star B, but appears brighter because it is closer.
Ratio 1:2

Question 3 - Worked out to 1/20th .

Just need assistance to set these out correctly - and also make sure that they are correct.

 

[zebra1707]

Any thoughts?

 

[Redbelly98]

The Attempt at a Solution

Question 1 - Worked out to - by moving Star A 10 times further away we have diminished the apparent brightness of Star A by a factor 10 x10 = 100 so that it now matches the brightness of Star B.

Question 2 - Worked out to - Luminosity of A
Luminosity of B = (½)2 x 2 = ½

This means that Star A really only has half the luminosity of Star B, but appears brighter because it is closer.
Ratio 1:2

Looks good so far.

Question 3 - Worked out to 1/20th .

So are you saying that B appears to be 20 times dimmer than A? I will suggest rethinking this one. Hint: distance is not a factor here, since it is the same for both stars.

 

[arunma]

Zebra, you seem to be really close on the last one. When distance is constant, the apparent brightness is just proportional to the luminosity.

 

[zebra1707]

Many thanks for the replies.

Yes, I think I understand what you are saying about question 3.

Again, many thanks for the replies.

Cheers