Knowing that the luminosity of main sequence stars with masses from 0.5 to 10 solar masses is proportional to the fourth

Knowing that the luminosity of main sequence stars with masses from 0.5 to 10 solar masses is proportional to the fourth power of mass (L ~ M ^ 4), you will get the form of the dependence of the lifetime of such stars on the mass. Calculate the lifetime of stars with masses of 0.5; five; 10 masses of the Sun, knowing that the age of the Sun is now estimated at 5 billion years and it will be on the main sequence for so many years.

The fuel supply in a star is proportional to its mass, and the rate of fuel depletion is proportional to the luminosity. Hence, t – M / L- M ~ 3, the Sun’s lifetime is about 10 billion years. Hence, for a star with a mass of 0.5 solar masses, the lifetime is ~ 80 billion years; for a star with a mass of 5 solar masses – = 80 million years; for a star with a mass of 10 solar masses – -10 million years.