Activity 1: Determining the Earth's
Average Density | ||||

A clue to the composition of the Earth can be obtained from its density (), the ratio of mass to volume: | ||||

| (Eq. 1) | |||

The Earth is very nearly a perfect sphere. Its volume can be approximated by | ||||

(Eq. 2) | ||||

where r is
the radius of the Earth, 6371 km. By substituting Eq. 2
for volume in Eq.
1, we can
calculate
planet’s average density | ||||

(Eq. 3) | ||||

We can’t weigh
the Earth on a scale,
but we can estimate
its mass (M) from measurements of gravitational acceleration (g) by | ||||

(Eq. 4) | ||||

where G is the
gravitational constant, 6.673 × 10^{-11} m^{3}/kg·s^{2}. Gravitational
acceleration g can be measured directly; it is related to the period T (time required to
complete one swing) of a pendulum and pendulum length L by: | ||||

(Eq. 5) | ||||

By measuring T,
g and M can be calculated. With Earth’s volume and mass known,
its average
density can be calculated from Eq. 3. Accurate measurements of a pendulum’s period show that
gravitational acceleration
at Earth’s surface
is approximately 9.8 m/s^{2}. | ||||

Any model of Earth’s interior should have the correct mass. After calculating the mass, use the Java applet below to create some density models of Earth’s interior. | ||||

| ||||

Copyright Houghton Mifflin Company. All
Rights Reserved. |