Q:  The mass of the Sun is M = 1.99 x 10^30 kg,
          and its luminosity is L = 3.8 x 10^26 Joules/second.
          Assume that 90 percent of this is hydrogen.  Assume further
          that all of the hydrogen may be converted into helium
          (which is quite an overestimate).

      How long could this fusion power the Sun's current luminosity?


          If 0.7 percent of the hydrogen is turned into energy, the
          total energy released would be


              E(tot)  =  [ lost mass ] * c^2

                      =  [ 0.007 * 0.90 * 1.99 x 10^(30) kg ] * (3 x 10^8 m/s)^2

                      =  1.14 x 10^(45) J


          If the energy is radiated away at the Sun's current luminosity,
          it could last

                          E(tot)        1.14 x 10^(45) J
                T     =  ---------  =  -------------------
                            L           3.8 x 10^(26) J/s


                      =  3.0 x 10^(18) s 

                      =  9 x 10^(10) yr


          And 90 billion years is much more than the current age of
          the solar system (about 4.5 billion years), so fusion
          will solve the problem.