# Mass-Luminosity-Time relation (Astronomy)

1. Nov 18, 2009

### Unto

1. The problem statement, all variables and given/known data
The lifetime of the sun on the main sequenceof the hertzprung-russel diagram is estimated to be 10^10 years. Assuming that the luminosities of stars on the upper diagram main sequence vary as mass^4, estimate the solar mass of a star for which it's main squence lifetime is 10^6 years.

2. Relevant equations
L = k M^b
T = kM / L = k M^1-b
T = k M^-2

'=k' is a subsitute for the proportional symbol
b = beta

3. The attempt at a solution

I know the star is going to be heavier, but I'm not given any values for luminosity. And when I try to equate time to mass I get funny answers. A push in the right direction here?

2. Nov 18, 2009

### Unto

K the sun's luminosity is 3.9E26 W, I figured I will use this to help me solve the answer.

3. Jan 1, 2012

### Jenab6

The mass luminosity relation isn't a physical model; it's an empirical curvefit. The best fit isn't necessarily a pure power function.

It can be

L/L๏ = K (M/M๏)^a

But K isn't required to be 1.

It can also be more complicated, such as

L/L๏ = K₁ (M/M๏)^a₁ + K₂ (M/M๏)^a₂

For example, the mass luminosity relation for the mass interval from 2 suns to 20 suns is approximately

L/L๏ = 1.505964 (M/M๏)^3.5 − 0.0252982 (M/M๏)^4.5