Measuring the Size of the World with Tomato Stakes
by Dr. Paul Romani (NASA-Goddard Space Flight Center), Kathleen Hackett (Glenarden Woods Elementary School), and Tamara Kaplan (Wildwood Elementary School).

Fifth grade students at Glenarden Woods Elementary Magnet School for Talented and Gifted (TAG) Students, Glenarden, Maryland this year studied ancient Egypt in a thematic unit that involved language arts, social studies, and art. To expand the unit to include math and science, we searched the World Wide Web for possible resources. We contacted Dr. David Dearborn via his e-mail address posted on the Center for Archeoastronomy's Web site. He suggested duplicating Erastosthenes's, a Greek who lived and experimented in Egypt, measurement of the circumference of the Earth. In its simplest form this means measuring the Sun's elevation at solar noon at two different latitudes on the same day, subtracting the difference which gives the latitudinal separation, and combining that with the north-south distance to compute the circumference of the world.

Kathleen Hackett, language arts teacher at Glenarden, then contacted Tamara Kaplan, a 4th grade teacher at Wildwood Elementary School in Amherst, Massachusetts who agreed to join the project. The Wildwood students are not part of a TAG program, showing that any children can do this, under the proper direction. At both schools students read "The Librarian Who Measured the Earth" by Kathryn Lasky (Publisher: Little, Brown and Co.) for background information. The next step, waiting for a sunny day in both locations proved to be a challenge. We were fortunate that the teachers had some autonomy in their schedule and could be flexible. Two days back to back in late May were used. The solar declination did not change appreciably between the days and did not affect our results.

To replicate Erastosthenes's observation, the students measured the length of shadow cast by a gnomon at solar noon. The students were placed into groups of four. At Glenarden, tomato stakes were used to cast the shadows. The children then placed meter sticks on the ground so that shadow fell on top of the meter stick. The students started measuring the length of the shadow about a half hour before solar noon and took measurements every five minutes (to keep them busy and out of trouble). At Wildwood the students used metal posts that had been cemented into the ground. They put white construction paper on the grass to allow them to see the shadow better. They were fascinated to see the shadow change in length and in position. This was also noticed by the students at Glenarden, some complained about having to move the meter stick because the shadow kept moving!

The following day, the students used the shadow measurements to determine the Sun's elevation. The students drew similar triangles, i.e. right triangles that preserved the ratio of gnomon height to shortest shadow length. Then, using a protractor, they measured the angle corresponding to the Sun's elevation in their similar triangle. Multiplemeasurements of the angle were made and the results were averaged. The data from Glenarden Woods had a fair amount of random noise, but the average was close to the correct answer. The students at Wildwood made two measurements of Sun's elevation with the second set being more accurate. Both groups' Sun elevations were high by about one degree, but since the numbers were being subtracted from one another this did not matter.

To determine the north-south distance between Wildwood Elementary and Glenarden Elementary, the students measured the north-south distance between Boston, Massachusetts and Washington, DC on a map (Boston is at the same latitude as Amherst and Washington, DC is close to Glenarden). A map with a latitude-longitude grid on it would have helped as students would have been able to measure the north-south distance parallel to the longitude lines.

The students' final measurement error of the circumference of the Earth was on the order of Erastosthenes's error (15%) and mainly came from problems with the map.

This was a great activity for the children to learn and apply science process skills. Children need to have had some prior experiences with geometry; similar figures, using a protractor, measuring degrees in a circle; and in decimals: adding decimal numbers, finding averages, dividing decimals. It gave them a chance to collect and process data on a real life problem. They had to: assess the data quality, communicate their findings with others, and use the data they got from their teammates to come up with their final calculations.

The Goddard Space Flight Center Public Affairs Office rewarded each student with a GOES Weather Satellite picture of the Earth for measuring the circumference of their home planet. For more information on this effort, contact:

Dr. Paul Romani
Mail Code 693
NASA-Goddard Space Flight Center
Greenbelt, MD 20771
E-mail		romani@gsfc.nasa.gov

Kathleen Hackett
Glenarden Woods Elementary School
Glenarden Pkwy at Echols Ave.
Glenarden, MD 20706
E-mail		74271.2302@Compuserve.com

Tamara Kaplan
59 Taylor Hill Rd. 
Montague, MA 01351. 
E-mail		kdanford@k12.oit.umass.edu