Measuring the Earth

High School Lessons || Contents

An Explorer lesson in which students use shadows and geometry to measure the earth.

Download a Claris Works or Acrobat file from the Explorer site. Also information on grades, availability, description, curriculum, process skills, author, and publisher.

Author: Jane Rich, Shawnee High School, Shawnee, OK

Grade Level/Subject: 9-12



Objective(s): As a result of this activity, the students will:

  1. Work effectively in a small group to take accurate measurements at a specific time.
  2. Use their knowledge of geometry and trig. to determine the measure of an angle.
  3. Use significant digits in their reports.
  4. Calculate percent error.
  5. Use their research skills to determine accepted values.
  6. Understand the value of cooperation in achieving a common goal.


Activities and Procedures:

  1. Contact a class directly north or south of you (in a different state if possible) and set a specific date and time to take the measurements.
  2. Divide the class into groups and practice at least once before the day of the activity. They are to measure the height of an object ( a pole is good) and the length of its shadow at a specific time. I have them start 15 minutes before the stated time.

  3. Assign several people to research the circumference of the earth and others to find several ways to determine the distance from your school to the other group's school (maps, auto clubs, etc.). Eratosthenes had a slave to pace off the distance between the two cities and report back to him.

  4. The measure of the angle is found by dividing the length of the shadow by the height of the object on your scientific calculator and then pushing 2nd function tangent. However, this is not the central angle. The angle from the other school must be subtracted from your angle and the absolute value of this difference is the central angle. The circumference of the earth can them be calculated by setting up a ratio and solving for the circumference.
        central angle       distance from schools
       ---------------  =  -----------------------
         360 degrees           circumference
  5. The students will have to decide how many significant digits to use in their results and then calculate the percent error from the value they found in their research.

Tying it all together:

  1. Discuss the sources of error and the fact that your results depend on other people making accurate measurements.

  2. I like to show the first tape of the "Cosmos," which tells about Eratosthenes.

  3. The next activity might be to measure the height of our flagpole indirectly.
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