Assume that the Sun when it first formed was composed of 70 percent hydrogen. How many hydrogen nuclei were there in the Sun at that time? How much energy would ultimately be released if all of the hydrogen nuclei fused into helium? Astrophysicists have predicted that the Sun can radiate energy at its current rate until about 23 percent of the hydrogen has been “burned.” What total lifetime for the Sun does that prediction imply? Compare these results with the corresponding ones from Problem 13-29.

Problem 13-29

When the Sun was formed, about 75 percent of its mass was hydrogen, of which only about 13 percent ever becomes available for fusion. (The rest is in regions of the Sun where the temperature is too low for fusion reactions to occur.) M_Θ = 2 x 10³⁰ kg and the Sun fuses about 6 x 10¹¹ kg/s.

(a) Compute the total mass of hydrogen available for fusion during the Sun’s lifetime. 

(b) How long (in years) will the Sun’s initial supply of hydrogen last? 

(c) Since the solar system is currently about 4.6 x 10⁹ y old, when should we begin to worry about the Sun running out of hydrogen for fusion?