Finding a constant of proportionality from a mass luminosity relation

[ppy]

Homework Statement

For main sequence stars, the mass–luminosity relation can be approximated by L\proptoM^{3.5}
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^{26}W and
M = 2x10^{30} kg

 

[Ibix]

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?

 

[ppy]

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\proptoM^{3.5} this is the same as L=kM^{3.5} so k=L/M^{3.5} and do I just substitute in the values for the luminosity of the sun and the mass of the sun?

 

[Ibix]

Bingo. What do you get?

 

[ppy]

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.

 

[ppy]

which doesn't make sense help!

 

[Ibix]

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?

 

[ppy]

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

 

[Ibix]

So in solar units the constant is...

 

[ppy]

are you saying in solar units the constant is 1?

 

[Ibix]

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