Consider a simple model for the interior of the Earth: there is a spherical iron

Question

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= 8.90*10^3 kg/m^3 and ?1= 3.90*10^3 kg/m^3. The radius of the Earth is R = 6.40*10^6 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).

Explanation / Answer

?=-G?(?(r')/r)dv'

g=-??

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