# Finding a constant of proportionality from a mass luminosity relation

## Homework Statement

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

Ibix
2020 Award
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?

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$\propto$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?

Ibix
2020 Award
Bingo. What do you get?

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.

which doesn't make sense help!!

Ibix
2020 Award
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?

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
2020 Award
So in solar units the constant is...

are you saying in solar units the constant is 1?

Ibix