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= 8.70×103 kg/m^3 and ?1= 4.40×103 kg/m^3. The radius of the Earth is R = 6.40×106 m.
(a) First, calculate the mass of the Earth. [Hint: Use G and g.]
(b) Calculate the radius a of the iron core.
(c) Derive the graviational field g(r) as a function of r. Hand in a numerically accurate graph of g(r). The value at r=R must be 9.81 m/s^2.
(d) Calculate g(a).