Consider a simple model for the interior of the Earth: there is a spherical iron core with constant mass density ?0 and radius a; outside the core is "rock" with constant density ?1. Use these values for the densities: ?0= 8.30×103 kg/m3 and ?1= 4.50×103 kg/m3. The radius of the Earth is R = 6.40×106 m.
(a) First, calculate the mass of the Earth.
(b) Calculate the radius a of the iron core.