Life expectancy of stars: The life expectancy E of a main-sequence star12 depends on its mass M. The relation is given by where M is solar masses and E is solar lifetimes. The sun is thought to be at...

Life expectancy of stars: The life expectancy E of a main-sequence star12 depends on its mass M. The relation is given by

where M is solar masses and E is solar lifetimes. The sun is thought to be at the middle of its life, with a total life expectancy of about 10 billion years. Thus the value E = 1 corresponds to a life expectancy of 10 billion years.

a. Does a more massive star have a longer or a shorter life expectancy than a less massive star?

 b. Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica?

 c. Express using functional notation the life expectancy of a main-sequence star with mass equal to 0.5 solar mass, and then calculate that value.

d. Vega is a main-sequence star that is expected to live about 6.36 billion years. What is the mass of Vega?

 e. If one main-sequence star is twice as massive as another, how do their life expectancies compare?