Department of Chemistry
Ohio Northern University
Ada, Ohio 45810
This was edited on 12 January 2015 to update a link.
I was watching a repeat of Carl Sagan’s television series, Cosmos, which prompted me to post this.
This was written in 1989 and was accepted for publication but was never actually published. It was written before the Internet became what it is today; interestingly enough, the Internet made the communications that I suggested in the paper even more plausible (which, in fact, actually did happen as I will note at the end of this blog).
In teaching earth science, Eratosthenes’ work in determining the circumference of the earth in 240 B.C. (approximately) is often discussed (a description of this calculation is included at the end of the paper). In his PBS series, “Ring of Truth”, Philip Morrison demonstrated a way that Eratosthenes’ experiment could be repeated by elementary, middle school, or junior high students.
Dr. Morrison’s procedure was to sight the star Antares at a specific time of the evening, drive south for one day, and repeat the measurements at the same time the next day. Noting the difference in the angle of altitude and the distance driven between the two sightings, the circumference of the earth could then be determined. Dr. Morrison suggested that a group of friends could do this on an overnight trip. (In his presentation, Dr. Morrison drove from the Kansas-Nebraska state line south on U. S. 283 to the Kansas-Oklahoma state line. As you can see, this is a relatively straight section of road, with just one “hitch” in it. It provides the base line that is needed for the project.
The focus of this paper is to present an alternative to Dr. Morrison’s suggestion which has distinct advantages and avoids the time and expenses of an overnight trip. The procedure need not be done by one class alone. Students could contact students in another school in a city some distance away and ask them to participate in the project. The two classes could then decide which star to look at and the time to make the appropriate measurements. After mailing the appropriate information to the other class, each student participating can then determine the circumference of the earth.
What is gained from this exercise? Dr. Morrison used this demonstration as part of the episode in his series on mapping. In discussing this in class, students may want to look at why only schools north or south of their location and not east or west can be used in this experiment. As in the television series the way mapping is accomplished is a natural follow-up to this exercise. In addition, this exercise illustrates the idea of the precision and accuracy of measurements in general. As such, it can be used by other science classes when discussing measurement. Many texts point out Eratosthenes’ measurements compare favorably with the accepted value for the circumference of the earth, yet I wonder if student understand the relative sizes involved or the relevance of the original experiment itself. Repeating Eratosthenes’ experiment can give some meaning to what is read.
Other non-science skills are also required. In order to accomplish this experiment, a science class in another city is needed. This requires students to write other students. We want our classes to be inter-disciplinary in nature yet we seldom find opportunities for such efforts. Writing another science class offers a chance to use communication skills as part of a science project. It also shows learning as a cooperative endeavor rather than a competitive one.
Students have to make several decisions in this project. For example, how far apart do the cities have to be? Which city or town should they select? Why does the selected city have to be north or south instead of east or west of their home town? What do they write to their new partners in science?
This exercise is designed to look at one specific idea students read about in their texts. Doing it as suggested offers opportunities to move science outside the boundary of the classroom and give students a chance to become acquainted with other students whom they might not normally meet.
There are benefits for the teacher as well. This exercise gives teachers the chance to collaborate on a project beneficial to all involved. Often, because of time and/or money, teachers become frustrated in their efforts to illustrate science in their everyday life. Combining the resources of two classrooms may overcome some of these frustrations and difficulties.
It is also possible that other multi-class projects could be done in this manner. Studies in biology or geology that require different localities would be likely candidates.
I did nothing with this particular piece after it was tentatively accepted for publication. It was too short for a regular piece and there were no other similar articles at the time to justify the page space. So it got “shelved”.
But when the Internet came along, things began to happen. There was an effort that utilized simple e-mail based communications to transfer data that ultimately transformed into “The Noon Observation Project”. I do not know if this is still an on-going project since the dates on the web page are from 1996 and the link to 1997 does not work.
Here is a description of Eratosthenes’ calculations:
Eratosthenes used geometry to estimate the circumference of the Earth.
Eratosthenes measured the altitude of the noontime sun at Alexandria at its maximum on June 21st. On that date, the Sun is directly overhead at noontime at Syene, in southern Egypt (latitude = 23.5 degrees north).
The zenith distance is the angle from the zenith to the point where the Sun was at noon; it is also 90 degrees minus the altitude. At Syene, the zenith distance was 0 degrees; at Alexandria it was about 7 degrees.
He knew how far it was from Alexandria to Syene (as Carl Sagan noted in his own television series, Cosmos, Eratosthenes paid someone to determine the distance), so he used geometry and the difference in zenith angle to estimate the size of the Earth.
Eratosthenes also measured the tilt of the Earth axis by 23.5 degrees, which gives us the seasons