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Estimate lifetime of a star

  1. Jan 5, 2013 #1
    1. The problem statement, all variables and given/known data
    If the exponent, α, in the mass-luminosity relationship is 3.0, estimate the lifetime
    of the above star. (You can assume that the Sun’s lifetime is 1 x 10^10 years).

    2. Relevant equations

    L*/Lsun = (M*/Msun)^α
    lifetime ∝ M/L ∝ M^-2

    3. The attempt at a solution

    The solution is given as:

    For a 20Msun star

    Lifetime = 20^-2 x 1 x 10^10 yrs
    = 25 x 10^6 yrs

    Could anyone explain to me how this solution has been arrived at?

    Thank you.
  2. jcsd
  3. Jan 5, 2013 #2


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    Science Advisor

    What you have written doesn't make much sense. Looking at "L*/Lsun = (M*/Msun)^α", since you don't tell us what the letters stand for, my first guess would be that L* is the lifetime sought, that Lsun is the lifetime of the sun (10^10 years), that M* is the mass of the star and Msun is the mass of the sun. But then you say "lifetime ∝ M/L ∝ M^-2" so apparently "L" is NOT the lifetime of the star. Then I don't know what that "L" could stand for. Can you clarify?
  4. Jan 5, 2013 #3
    Sorry about that.

    L stands for luminosity, as far as I'm aware

    L* the luminosityof the star in question. Lsun that of the sun.
    'M' I believe stands for the mass.
  5. Jan 5, 2013 #4


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    Gold Member

    You don't care about the luminosity here, so the relevant equation is:
    lifetime ∝ M-2
    So a star with 20 times that of the sun will have 20-2 = 1/400 times the lifetime.
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