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 p0 and radius a; outside the core is "rock" with constant density p1. Use these values for the densities: p0= 8.90*10^3 kg/m^3 and p1= 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

similar problem and solution:

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

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