**ESSAYS FROM ARCHAEOASTRONOMY & ETHNOASTRONOMY NEWS, THE QUARTERLY BULLETIN OF THE CENTER FOR ARCHAEOASTRONOMY **

Number 21 September Equinox 1996

**
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