Calculating the Earth's Circumference

Georgia Perimeter College

Objectives

Use simple measurements and calculations to determine the circumference of the Earth without leaving the lab.

Preassessment

Explain how you might measure the size of the Earth.  Write it on a piece of paper.  Crumple it up, and throw it into a pile in the middle of the room. 
Select a paper, open it and read it.  (If you get your own, throw it back and take another one.)

Materials

Meter stick
Masking tape
String (at least twice as long as the stick)
Protractor
Globe or world atlas

Background

The circumference of the Earth was measured by Eratosthenes, a Greek mathematician, geographer and astronomer who lived 276 - 195 BC. He knew that at noon on the summer solstice in Syene (in southern Egypt), the Sun shone directly down a deep vertical well, illuminating the bottom. Eratosthenes recognized that the Sun must be directly overhead at Syene on the summer solstice.

In Alexandria, Egypt, north of Syene, he saw that the sun was not overhead directly at that time because a vertical post cast a shadow. Eratosthenes measured the angle of the shadow (7.2°), and knowing the distance from Alexandria to Syene (5000 stadia), he calculated the circumference of the Earth.

He knew from geometry that the angle he measured was equal to the angle between Alexandria and Syene, as measured from the Earth's center. Because the arc of the angle he measured was 1/50 of a circle, he multiplied 5000 stadia by 50. His result, 250,000 stadia (or about 46,250 km), is surprisingly close to modern measurements of the circumference of the Earth (about 40,024 km on average).

His calculation was based on two assumptions - that the Earth is round and that the Sun's rays are essentially parallel. 

Activity

This experiment can only be done at solar noon twice a year; at the spring or vernal equinox (March 20) and at the autumnal equinox (September 22). These are the two times each year that the Sun is directly over the equator.  You can do the experiment a day or two before or after the equinox to allow for cloudy days or class schedules.

By measuring the length of a shadow, and by knowing the distance that you are from the equator, you can determine the circumference of the Earth.

Procedure
  1. Tape a string to the very end of a meter stick.
  2. Place the meter stick vertically into the ground. Make sure the stick is in a true vertical position.  You can do this by using a weight on a string as a plumb bob.
  3. Determine "solar noon" for your location and time zone by consulting your local newspaper for the sunrise/sunset times and calculating the midpoint.
  4. At "solar noon" extend the sting at an angle where it does not make an shadow on the ground. Tape it to the ground. Be careful to not pull the meter stick out of its true vertical position.
  5. Using the protractor, measure the angle between the meter stick and string.
  6. Using the globe or atlas, determine the distance your location is from the equator.  Or find the distance with the computer using the following procedure

    a.  Go to http://local.live.com and find your location. 
    Get the latitude and longitude by going to "Share" and clicking on "View Permalink", and by looking for the latitude and longitude numbers in the permalink address. 
    Or use a GPS (Global Positioning System) device.

    b.  Find the latitude and longitude of the position on the equator nearest to you.  Latitude is 0 degrees, longitude is your longitude.

    c.  Go to a website that will calculate the distance between the two points, or use the calculator below.

        How far are you from the equator? __________________________ km
      

Distance Calculation

Enter your coordinates (latitude and longitude) into the text boxes.  You can use a variety of formats:

  • Degrees-minutes-seconds suffixed with N/S/E/W (e.g. 40°44′55″N, 73 59 11W), or
  • Signed decimal degrees without compass direction, where negative indicates west/south (e.g. 40.7486, -73.9864):
  • You can also convert between degrees-minutes-seconds and decimal degrees (like you get from a GPS unit) using the second calculator below.
     

        Latitude 1: Longitude 1:

        Latitude 2: Longitude 2:

       

Convert between degrees-minutes-seconds & decimal degrees

Latitude

Longitude

Handy Reference:
Degrees: 1° ≈ 111 km

Minutes 1′ ≈ 1.85 km

0.001° ≈ 111 m

Seconds 1″ ≈ 30.9 m

0.00001° ≈ 1 m

 

  1. Once you know your distance from the equator, use the formula below to calculate the circumference of the Earth:
    2.

        To solve for the circumference, multiply your distance from the equator by 360 and divide by the measured angle.


        What is the result of your calculation for the circumference of the Earth? _____________________________


The actual circumference around the poles is 24,860 miles (40,009 km). The circumference around the equator is slightly larger, 24,902.4 miles (40,076.5 km). This is due to the Earth's rotational speed and the fact that the Earth's outer core is liquid and not solid.

  1. Your answer should be similar , but will be slightly different.  List the possible sources of error in your work.

    _____________________________

        _____________________________

        _____________________________
 

 


 

Return to Integrated Science 2001 page

Return to Georgia Geoscience Online

Content provided by the National Weather Service http://www.srh.noaa.gov/jetstream/global/ll_shadow2.htm
Script for distance calculation and latitude/longitude calculations is from http://www.movable-type.co.uk/scripts/latlong.html, copyright 2002-2007 Chris Veness
Some content provided by Pamela Gore, Georgia Perimeter College

Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created August 12, 2007
Links updated September 22, 2008