Q:  What is the amount of GPE released by the contracting Sun?


                   0.6 * 6.67 x 10^(-11) * (1.99 x 10^(30))^2 
           GPE  =  -------------------------------------------
                             6.95 x 10^(8)  m


                =  7.2 x 10^(41) J

          
            That sounds like a lot of energy.


  Q:  The current luminosity of the Sun is about 3.8 x 10^26 J/s.
            How long could this GPE power the Sun?


            This GPE could power the current Sun for a time of


                        7.2 x 10^(41) J
                T   =  -----------------  =  1.9 x 10^(15) s
                       3.8 x 10^(26) J/s


                                          =  6 x 10^7   years


             Whoops.  60 million years is a long time -- but not long enough.