Teaching Physics with the Physics Suite

Edward F. Redish

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Using the moon to find the density of the earth

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-m2/kg2.

b. Using your result for part (a), and the fact that the volume of a sphere is (4/3)πR3, 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