# 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$\propto$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

## Answers and Replies

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$\propto$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?

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!!

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

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