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Mass-Luminosity-Time relation (Astronomy)

  1. Nov 18, 2009 #1
    1. The problem statement, all variables and given/known data
    The lifetime of the sun on the main sequenceof the hertzprung-russel diagram is estimated to be 10^10 years. Assuming that the luminosities of stars on the upper diagram main sequence vary as mass^4, estimate the solar mass of a star for which it's main squence lifetime is 10^6 years.



    2. Relevant equations
    L = k M^b
    T = kM / L = k M^1-b
    T = k M^-2

    '=k' is a subsitute for the proportional symbol
    b = beta


    3. The attempt at a solution

    I know the star is going to be heavier, but I'm not given any values for luminosity. And when I try to equate time to mass I get funny answers. A push in the right direction here?
     
  2. jcsd
  3. Nov 18, 2009 #2
    K the sun's luminosity is 3.9E26 W, I figured I will use this to help me solve the answer.
     
  4. Jan 1, 2012 #3
    The mass luminosity relation isn't a physical model; it's an empirical curvefit. The best fit isn't necessarily a pure power function.

    It can be

    L/L๏ = K (M/M๏)^a

    But K isn't required to be 1.

    It can also be more complicated, such as

    L/L๏ = K₁ (M/M๏)^a₁ + K₂ (M/M๏)^a₂

    For example, the mass luminosity relation for the mass interval from 2 suns to 20 suns is approximately

    L/L๏ = 1.505964 (M/M๏)^3.5 − 0.0252982 (M/M๏)^4.5
     
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