Finding a constant of proportionality from a mass luminosity relation

1. Oct 13, 2013

ppy

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

For main sequence stars, the mass–luminosity relation can be approximated by L$\propto$M$^{3.5}$
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

2. Oct 13, 2013

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?

3. Oct 14, 2013

ppy

as L$\propto$M$^{3.5}$ 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?

4. Oct 14, 2013

Ibix

Bingo. What do you get?

5. Oct 21, 2013

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.

6. Oct 21, 2013

ppy

which doesn't make sense help!!

7. Oct 21, 2013

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?

8. Oct 22, 2013

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

9. Oct 22, 2013

Ibix

So in solar units the constant is...

10. Oct 23, 2013

ppy

are you saying in solar units the constant is 1?

11. Oct 23, 2013

Ibix

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