Consider a star whose density increases toward its center. If we model this star as a series of concentric shells (each shell having its own uniform density), then the equation of mass continuity relates the mass in each shell to the density and volume of the shell. The star has the following two regimes: Core: ⍴r = ⍴0 from r = 0 to r = r0 Envelope: ⍴r = ⍴0(r/r0)-2 from r = r0 to r = R Integrate the equation of mass continuity (see provided image) over the appropriate ranges to find expressions for the masses in the core and in the envelope. Add the two expressions to find an alegbraic expression for the total M inside R.

Consider a star whose density increases toward its center. If we model this star as a series of concentric shells (each shell having its own uniform density), then the equation of mass continuity relates the mass in each shell to the density and volume of the shell. The star has the following two regimes: Core: ⍴r = ⍴0 from r = 0 to r = r0 Envelope: ⍴r = ⍴0(r/r0)-2 from r = r0 to r = R Integrate the equation of mass continuity (see provided image) over the appropriate ranges to find expressions for the masses in the core and in the envelope. Add the two expressions to find an alegbraic expression for the total M inside R.