# Homework Help: 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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted