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Luminosity of a star

  1. Nov 22, 2003 #1
    Here are a few more questions that I really need help on, thanks!




    3. A Cepheid variable star is observed in the nearby galaxy M31. Its period of variation
    is measured to be 40 days. Using the period - luminosity relation given in the table
    below, what is the luminosity of the Cepheid in solar luminosities?
    Period Luminosity
    (days) (solar luminosities)
    2.5 645
    4.0 1120
    6.3 2000
    10.0 3550
    15.8 6310
    25.1 11500
    40.0 20900
    63.1 38000

    4. For the Cepheid in M31, what is its luminosity in ergs/sec? (Recall that the solar
    luminosity is 3.85 x 1033 ergs/sec.)


    5. The Cepheid in M31 has its apparent brightness measured at 1.06 x 10-12 ergs/sec/cm2.
    The inverse square law of light may be written as
    b = L ÷ 4 pi r^2
    Where b is the apparent brightness, L is the luminosity and r is the distance.
    How far away is the Cepheid in centimeters? Convert your answer to parsecs by
    knowing that one parsec contains 3.09 x 1018 centimeters.
     
  2. jcsd
  3. Nov 22, 2003 #2
    My biggest problem with these is that I'm totally lost. My professor assigns these problems, but our book and his notes don't show how to do them.
     
  4. Nov 22, 2003 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    What? You mean your professor actually expects you to think for yourself? How evil of him.

    Okay, that bit of sarcasm off my chest, in problem 3 you are given a table:
    (days) (solar luminosities)
    2.5 645
    4.0 1120
    6.3 2000
    10.0 3550
    15.8 6310
    25.1 11500
    40.0 20900
    63.1 38000

    and asked to determine the "luminosity" if "days"= 40. This is purely a test of how you can read a table? (emphasis mine.)

    Once you know the number of "solar luminosities" you are told that each solar luminosity is 3.85 x 1033 ergs/sec. Okay, convert your solar lumnosities to ergs/sec. (Hint: if you knew each hamburger cost $1.50, how would you find the cost of 6 hamburgers?)

    Finally you are given a formula: b = L ÷ 4 pi r^2
    You know b (apparent brightness) is 1.06 x 10-12 ergs/sec/cm2.
    You know L (luminosity) from problem 3 and you know (I hope!) that pi is approximately 3.1416. Plug them into the equation and solve for r.

    By the way, do you recognize 4 pi r^2 as the formula for surface area of a sphere? In other words, that formula says that after the light has gone a distance r, the light, L, has spread out over the surface of that sphere giving the apparent brightness, b, for someone at one point on that sphere.
     
    Last edited: Nov 22, 2003
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