A CIESE Collaborative Project

School's Report Gallery
Fall, 2006

School: A. R. Gould, South Portland, Maine
Final Report
Summary:
The class enjoyed the project. It was great to get outside on a sunny day. We learned alot about the relationship between the earth and the sun. We were particularly surprise at how quickly the shadow location changed as we were measuring it.

We were also surprised that our measurements were accurate enough to calculate the earth's circumference so accurately.

Students expressed that it was satisfying "to use math to solve an actual problem".

Data Recorded:
Friday, September 22, 2006

Site:

Equipment:
Gnomon was constructed using a one-meter-long dowel mounted through a wooden base (15" x 3.5" x 1.5"). The base of the meter-stick dowel was flush with whatever surface the gnomon rested upon.
• Compass
• Chart paper
• Pencils
• Watch

Here are some photos and diagrams:

a
 Observations: Students visited the site early in the morning of September 22nd to check weather conditions, view the site layoout to determine the best location for the gnomon, and to take measurements of the shadow positions (at 10 minute intervals) for practice and to experience taking such measurements (determining where the shadow ended, umbra and penumbra, etc.)

We talked about the the concept of solar noon and took information from the U.S. Naval Observatory website that displayed the sun's altitude and azimuth minute-by-minute throughout the day.

We decided that we would make measurements every minute beginning at 12:20 PM local time and continue marking readings through 12:40.

We began taking measurements at 12:25 PM. After the first few measurements, we realized that the location of the gnomon would soon fall under the shadow of the basketball backboard located to the south of the gnomon. We moved the gnomon and the recording sheet and used a compass to maintain the same orientation of the recording sheet.

From 12:25 to 12:33, we recorded shadow lenghts that varied from 96.4 cm to 96.9 cm. We believe that the variation was due to the subjective element of determining the end of the shadow as the light becomes diffuse at the end of the shadow.

Based upon a shadow length of 96.4 cm and a gnomon length of 100 cm, we constructed a scale right-angle triangle. Using a protractor, we determined that the shadow angle was 43 degees (the same as our latitude).

Using the pizza-slice analogy, an angle of 43 degrees represented 1 slice of the 8.37 slices that made the entire pie (360 degrees).

By taking the equator (shadow angle 0 degrees) as our reference point, we estimated the distance from the equator on a North-South line to be 4,779 km. To make that calculation, we used a conversion factor of 111 km for ever degree of latitude. (We learned that from a fifith-grade student's final report .)

Fram the data we calculated the circumference of the earth as being 39,950 km. That is within 0.1% of the actual value.

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