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Math Help - Magnitude Scales and log

  1. #1
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    Magnitude Scales and log

    The stellar magnitude scale compares the brightness of stars using the equation m_2 - m_1 = log(b_1/b_2). where m_2 and m_1 are the apparent magnitude of the two stars being compared (how bright they appear in the sky) and B_2 and B_1 are their brightness (how much light they actually emit). This relationship does not factor in how far from Earth the stars are.

    a) Sirius is the brightest-appearing star in our sky, with an apparent magnitude of -1.5. How much bright does Sirius appear than Betelgeuse, whose apparent magnitude is 0.12?


    My answer: (which is correct)

    Siruius appears to be 41.69 times brighter than Betelgeuse.


    b) The sun appears about 1.3 x 10^10 times as brightly in our sky as does Sirius. What is the apparent magnitude of the sun?

    I need help on this part.

    I subed in m_1 = -1.5 and (b_1/b_2) = (1.3 x 10^10)
    and then solved for m_2

    m_2 - m_1 = log (1.3x10^10)
    m_2 - (-1.5) = log (1.3 x 10^10)
    m_2 + 1.5 = log (1.3 x 10^10)
    m_2=log (1.3 x 10^10) - 1.5
    m_2=8.61

    therefore the apparent mag of the sun is 8.61.
    However, the back of the book says that it is -11.61.. How do I get it and what did I do wrong?
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    The stellar magnitude scale compares the brightness of stars using the equation m_2 - m_1 = log(b_1/b_2). where m_2 and m_1 are the apparent magnitude of the two stars being compared (how bright they appear in the sky) and B_2 and B_1 are their brightness (how much light they actually emit). This relationship does not factor in how far from Earth the stars are.

    ...

    b) The sun appears about 1.3 x 10^10 times as brightly in our sky as does Sirius. What is the apparent magnitude of the sun?

    I need help on this part.

    I subed in m_1 = -1.5 and (b_1/b_2) = (1.3 x 10^10)
    and then solved for m_2

    m_2 - m_1 = log (1.3x10^10)
    m_2 - (-1.5) = log (1.3 x 10^10)
    m_2 + 1.5 = log (1.3 x 10^10)
    m_2=log (1.3 x 10^10) - 1.5
    m_2=8.61

    therefore the apparent mag of the sun is 8.61.
    However, the back of the book says that it is -11.61.. How do I get it and what did I do wrong?
    In the given formula the order of the variables is

    LHS: m_2 , m_1

    RHS: b_1 , b_2

    In my opinion you changed the order of the variables because if (b1/b2)=1.3*10^10 then b_1 is referring to the sun and therefore m_1 is referring to the sun too.
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  3. #3
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    If b_1/b_2 = 1.3x10^10, then doesn't that mean that b_1 is the sun's brightness and b_2 is Sirius' brightness? Then you should have substituted -1.5 for m_2 instead of m_1.


    EDIT: beaten by earboth


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