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Finding a constant of proportionality from a mass luminosity relation

  1. Oct 13, 2013 #1

    ppy

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    1. The problem statement, all variables and given/known data

    For main sequence stars, the mass–luminosity relation can be approximated by L[itex]\propto[/itex]M[itex]^{3.5}[/itex]
    f) If luminosity and mass are both measured in solar units, what is the constant of
    proportionality? {2}

    I know that the luminosity value of the sun is 4x10[itex]^{26}[/itex]W and
    M = 2x10[itex]^{30}[/itex] kg
     
  2. jcsd
  3. Oct 13, 2013 #2

    Ibix

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    The "solar units" thing is telling you that mass is measured in terms of the mass of the Sun - such and such a star is seven times the mass of the Sun; M=7. The mass of the Sun is 1.

    Can you take it from there?
     
  4. Oct 14, 2013 #3

    ppy

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    as L[itex]\propto[/itex]M[itex]^{3.5}[/itex] this is the same as L=kM[itex]^{3.5}[/itex] so k=L/M[itex]^{3.5}[/itex] and do I just substitute in the values for the luminosity of the sun and the mass of the sun?
     
  5. Oct 14, 2013 #4

    Ibix

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    Bingo. What do you get?
     
  6. Oct 21, 2013 #5

    ppy

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    hi as L for the sun is 4x10^26 and M for the sun is 2x10^30 as the M is to the power 3.5 surely the constant is 0 as the denominator is huge compared to the numerator.
     
  7. Oct 21, 2013 #6

    ppy

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    which doesn't make sense help!!
     
  8. Oct 21, 2013 #7

    Ibix

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    It can't be zero. It can be very small. You can use the fact that (ab)n=anbn to take powers of the 4 and the 1026 separately.

    But before you do, read my first post again. What's the mass of the Sun measured in solar masses?
     
  9. Oct 22, 2013 #8

    ppy

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    we are not taking a power of (4x10^26) we are taking M=2x10^30 to the power 3.5 I know the mass of the sun is 1 in solar masses
     
  10. Oct 22, 2013 #9

    Ibix

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    So in solar units the constant is...
     
  11. Oct 23, 2013 #10

    ppy

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    are you saying in solar units the constant is 1?
     
  12. Oct 23, 2013 #11

    Ibix

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    Yes - well done. A smart choice of unit can make life a lot easier.
     
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