Q:  What is the value of the mass derivative in this shell?

    
        dM/dr  =   2.76 x 10^(16)    g/cm



  Q:  What is the mass interior to the next-inner shell?


        M_new  =  M_old              +  (dM/dr) * dr

               =  1.989 x 10^(33) g  +  (2.76 x 10^(16) g/cm) * (-7.1 x 10^7 cm)

               =  1.989 x 10^(33) g  -   1.96 x 10^(24) g

               =  1.988 899 999 8 x 10^(33) g


         A better way to describe the new mass is using the Q_M parameter.
            We can compute the change in QM with respect to radius
            via
                                change in mass     1.96 x 10^(24) g
                   delta_QM  =  --------------  =  ----------------
                                total mass         1.989 x 10^(33) g


                             =   9.85 x 10^(-10)


         Then we can compute the new QM value in the usual way.


         QM_new  =  QM_old   +   delta_QM


                 =  3.46 x 10^(-9)  +  9.85 x 10^(-10)

                 =  4.45 x 10^(-9)