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Finding a constant of proportionality from a mass luminosity relation

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  • #1
ppy
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Homework Statement



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
 

Answers and Replies

  • #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?
 
  • #3
ppy
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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?
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?
 
  • #4
Ibix
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Bingo. What do you get?
 
  • #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.
 
  • #6
ppy
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which doesn't make sense help!!
 
  • #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?
 
  • #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
 
  • #9
Ibix
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So in solar units the constant is...
 
  • #10
ppy
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are you saying in solar units the constant is 1?
 
  • #11
Ibix
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Yes - well done. A smart choice of unit can make life a lot easier.
 
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