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Determining distance using luminosity

  1. Feb 9, 2014 #1
    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.
     
  2. jcsd
  3. Feb 9, 2014 #2

    mfb

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    You made this more complicated than necessary, and the result looks wrong. All you need are relative values and the distance between earth and sun.

    A star at the same distance as our sun appears as bright as our sun, a star at 10 times the distance appears 10-2 as bright as our sun and so on. The result is very close (within 2%) of one of the given answers.
     
  4. Feb 9, 2014 #3
    so I can get the answer without using the formula I have?
     
  5. Feb 9, 2014 #4

    mfb

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    Yes.
     
  6. Feb 10, 2014 #5
    Ok, so I converted distance between Earth and Sun (1 AU) to light years and got 149,600,000 km.

    So if this star is 10^-20 as bright as the Sun, then it would be 10^20 times as farther?

    How do know if a star is 10 times the distance than its brightness is 10^-2?
     
  7. Feb 10, 2014 #6

    mfb

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    That is not converted to light years, it is converted to km.

    No.

    See the square in d^2 = L / (4*pi*B): If you increase d by a factor of 10, B goes down by a factor of 100.
    Alternatively: In 10 times the distance, the area (that gets light from the star) increases by a factor of 102=100, so the light per area goes down by the same factor.
     
  8. Feb 11, 2014 #7
    distance between Earth and Sun is 1 AU, which is equal to 1.58128451 × 10^-5 light years.

    Since I'm given the brightness times sun's brightness, I need to find the n times the distance using 10^-20 and then multiply 1.58128451 × 10^-5 light years by n, right?

    Also in my textbook, there is a formula for light-collecting area of a telescope that is d^2, where d is diameter and then when you square it, it gives you what the increase in brightness is in comparison to the other telescope.

    Would I be able to use that here? Say, d^2 = 10^-20 and then square root both sides and get 10^-10 and multiply that by the distance 1.58128451 × 10^-5 still gives me a wrong answer.
     
  9. Feb 12, 2014 #8
    got the answer lol, thanks for the help mfb
     
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