The library of Eratosthenes

september 26

Wednesday 26 September 2007 by perbosc


 Placerville, California, USA

  • Date : 26/09/2007
  • Shadow/Ombre : 85,9cm
  • Angle : 40°

    Herbert Green Middle School
    Placerville, California, USA
    Mrs. Muraoka’s 6th Grade Science Classes

    Our school is called Herbert Green, home to the Miners. Our school’s latitude is 38 degrees 42’ 34” N and our longitude is 120 degrees 49’ 45” W. The partner school for the 7th period class is College Antonin Perbosc in Lafrancaise, France. Their coordinates are 44 degrees 8’ N and 1 degree 15’ E. The partner school for the 4th period class is The Abba’s Orchard in Baugnon, Bukidnon, Philippines, located at 8 degrees 25’ N, 124 degrees 38’ E. We participated in the Noon Day Project and found the Earth’s circumference using Eratosthenes’ method.

     Procedure for measuring and finding the sun’s angle:

    The 7th period class did their measurements on September 26, 2007 and the 4th period class took their measurements on September 27, 2007, although the Autumnal Equinox was on Sunday, September 23, 2007. Our measurements were taken at 12:56 p.m., which was solar noon. To make our measurements we used these items. We needed a long sheet of paper, tape, a plumb bob, a meter stick attached to a bookend, a paper wedge, and a pencil. Measurements were taken by first laying the paper on the ground. Second, we used the tape to connect it to the ground. We then placed our yard stick at one end of the paper so that the shadow was atop the paper during our couple of minutes on the blacktop. The next step was to use the plumb bob to straighten the yardstick for the much needed accuracy. Now mind you, a plumb bob is simply a washer tied to the end of a very long string. At this point in time, we noticed that our yard stick was not on a flat surface. We needed our paper wedge under the bookend to make our meter stick perpendicular. A couple of people used some books to hold the paper or meter stick still. Last, but absolutely the most important part is measuring the shadows. The teacher gave us a signal to mark the end of the shadow and label it with the time. We took nine different measurements. We measured the shortest shadow in centimeters with a measuring tape. We found the average shadow length of the class by dropping our lowest length and highest length. Next, we found the mean of the numbers. On the white board, we then took the meter stick and held it vertically and marked the end. Then at a 90 degree angle to that line, we marked the average length of the shadow. We connected the mark from the end of the stick to the end of the shadow. This formed a triangle. We measured the top angle to find the angle of the sun. This angle was 39 degrees in 7th period and 40 degrees in 4th period.

     Calculations for finding Earth’s circumference:

    Period 7:

    Our partner city was Lafrancaise, France. We found the circumference of Earth by making calculations based on differences in our latitudes. 44.133 degrees N (Lafrancaise, France) minus 38.709 degrees N (Placerville, California, USA) equals 5.424 degrees. Then we changed the degrees to kilometers by multiplying by 111.325 km/degree. This distance equaled 603.827 km. Then we found the central angle by finding the difference in our partner school’s angle of the sun (44.5 degrees) and our angle of the sun (39 degrees). This equaled 5.5 degrees. We found there are 65.455 of our central angles in a circle by dividing 360 degrees by 5.5 degrees. Then we multiplied the distance between our school and our partner’s school by the number of central angles in 360 degrees to find the circumference. 603.827 km times 65.455 equals 39,523.496 km., which is our measurement for the Earth’s circumference.

    Period 4:

    We found the distance in latitudes between our school in Placerville, California, USA and our partner school, Abba’s Orchard in Baugnon, Bukidnon, Philippines by subtracting their latitude (8.419 degrees) from our latitude (38.709 degrees). This equaled a difference of 30.290 degrees. Then we multiplied 30.290 degrees by 111.325 km/degree which equals 3372.04 km. Then we found the central angle by subtracting the angle of the sun at our partner school from the angle of the sun at our school. 40 degrees minus 8.4 degrees equals 31.6 degrees. Next, we found the number of central angles in 360 degrees (the number of degrees in a circle) by dividing 360 by 31.6. This equaled 11.392 central angles in a circle. Then we calculated the Earth’s circumference by multiplying the distance between schools by the number of central angles: 3372.034 km times 11.392 equals 38,414.211 km.

     What we would do differently the next time:

    “I would make a stand that held the meter stick plumb to the ground so the measurements would be more accurate.”
    “Next time, we should get out side sooner so we have more time to set up our work stations.”
    “I would also like to do it on a day that wasn’t windy.”
    “We would try to make our timing and measuring more precise.”

     Highlights and what we learned from the Noon Project:

    “During the project I learned that it takes patience and responsibility to stay on task.”
    “I learned that Eratosthenes’ method was true that the Earth is round!”
    “Eratosthenes method actually worked!”
    "The angle of the sun (39 degrees) came out close to our latitude (38 degrees, 42 minutes, 34 seconds N).”
    “I learned you need to have a group effort.”
    “I also learned how to work better with others.”
    “I also learned that the earth moved a lot quicker than I thought because every time, I checked my shadow, it was a different measurement.”
    “I learned that the Earth is huge.”
    “I had fun taking measurements for an hour or so, and I got better at my math skills too.”
    “I learned that Eratosthenes was smart.”
    “Before I did this project I thought it would be impossible to figure out the circumference of the Earth. This project made it simple to figure out with its easy calculations.”

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