Dr. Aaron Titus | Department of Physics, High Point University PHY1050      Astronomy of Stars, Galaxies, and the Cosmos home | WebAssign | textbook | course calendar

## mass-luminosity relationship

To measure the mass of a star, we use Kepler's law and the momentum equation (or center of mass equation) for binary stars. When we graph the luminosity vs. mass of main sequence stars, we get something like the graph shown below.

This graph is called a log-log graph because the axis divisions are powers of 10. The slope of the line shown in this graph is 4. This means that the luminosity is proportional to mass to the 4th power. This is called the mass-luminosity relation and is expressed mathematically as

If you double the mass of a star, by what factor does its luminosity increase?

What if a star is not a binary star so you cannot measure its mass? Well, if it is a main sequence star, then we can use the mass-luminosity relationship to calculate its mass. But first, we would need to measure its luminosity.

Therefore, the mass-luminosity relation gives us the following method for calculating the mass of a main sequence star. (1) Determine the luminosity of a star and (2) calculate the mass of the star.

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