Question 13.2: The Density of the Earth Using the known radius of the Earth...

Conceptualize Assume the Earth is a perfect sphere. The density of material in the Earth varies, but let’s adopt a simplified model in which we assume the density to be uniform throughout the Earth. The resulting density is the average density of the Earth.

Categorize This example is a relatively simple substitution problem.

Using Equation 13.5, solve for the mass of the Earth:

g=G \frac{M_E}{R_E{}^2}     (13.5)

Substitute this mass and the volume of a sphere into the definition of density (Eq. 1.1):

\rho \equiv \frac{m}{V}     (1.1)