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 planetís average density

(Eq. 3)

We canít 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 m3/kg∑s2. 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 Earthís volume and mass known, its average density can be calculated from Eq. 3. Accurate measurements of a pendulumís period show that gravitational acceleration at Earthís surface is approximately 9.8 m/s2.
Any model of Earthís interior should have the correct mass. After calculating the mass, use the Java applet below to create some density models of Earthís interior.

copyright 1998, VisualEntities
To complete Activity 1, select one of these files:word.gif (252 bytes)
††

Copyright Houghton Mifflin Company. All Rights Reserved.
Terms and Conditions of Use, Privacy Statement, and Trademark Information