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a. Use your knowledge
of circular motion and Newton's law of universal gravitation to find an
equation expressing the mass of the earth, *M*, in terms of the
distance from the center of the earth to the moon, *r*, the period
of the moon in its orbit, *T*, and Newton's universal graviational constant, *G* ≈ 2/3 x 10^{-10} N-m^{2}/kg^{2}.

b. Using your result for
part (a), and the fact that the volume of a sphere is (4/3)π*R*^{3},
find an equation for the density of the earth ρ (rho)
in terms of *G*, *T*, *r*, and *R* = the radius of the earth.

c. Using your result for part (b), estimate the density of the earth. (The distance from the center of the earth to the moon is about one-quarter of a million miles.) How does this compare to the density of water? a rock? a chunk of iron?

The fact that if you know *G*, that standard astronomical knowledge such
as the distance to the moon and its period allows you to measure the mass of
the earth is why the experiment to measure *G*, done
by Cavendish in 1789,
is often referred to as "weighing the earth."

Page last modified November 24, 2009: GR10