It is straightforward to come up with a Main Sequence lifetime estimate. What we do is:

• Estimate the available fuel (energy)
• Use the observed rate the fuel is consumed (luminosity)

Available Fuel

Since the fusion of hydrogen into helium supplies the energy needed to power stars, it is clear that the amount of available fuel is going to be proportional to the amount of hydrogen in the star.

• Energy = f x e x M x c**2

Here, e is the efficiency of hydrogen burning, e ~ 0.007, and f is the fraction of the star which is available to be used for fuel in the Main Sequence phase of evolution, f ~ 0.1. We have that

• Energy = 1.3 x (M/M(sun)) x 10**51 ergs

Consumption Rate

The rate at which stars burn fuel is

• Luminosity ~ 4 x (M/M(sun))**4 x 10**33 ergs per second

Main Sequence Lifetime

The lifetime of a star on the Main Sequence is

• Lifetime = Energy / Luminosity = 3.2 x (M/M(sun))**(-3) x 10**17 seconds

  In years, this is

  • Lifetime = 10 x (M/M(sun))**(-3) billion years

Information provided by: http://zebu.uoregon.edu