Chapter 22, Problem 34E

The text explains that massive stars have shorter lifetimes than low-mass stars. Even though massive stars have more fuel to burn, they use it up faster than low-mass stars. You can check and see whether this statement is true. The lifetime of a star is directly proportional to the amount of mass (fuel) it contains and inversely proportional to the rate at which it uses up that fuel (i.e., to its luminosity). Since the lifetime of the Sun is about 1010 y, we have the following relationship:

   $T={10}^{10}\frac{M}{L}y$

where T is the lifetime of a main-sequence star, M is its mass measured in terms of the mass of the Sun, and L is its luminosity measured in terms of the Sun’s luminosity.

A. Explain in words why this equation works.

B. Use the data in Table 18.3 to calculate the ages of the main-sequence stars listed.

C. Do low-mass stars have longer main-sequence lifetimes?

D. Do you get the same answers as those in Table 22.1?