Eratosthenes Experiment
A Worldwide Science and Math Experiment
March 20, 2013

Dates to remember on this project: Project Summary:

This fun one day project allows students from all over the globe to calculate the circumference of the Earth by measuring the shadow of the sun, then using that measurement in a simple equation. Students and classes are encouraged to share their results with others by completing an experiment report form.

You may view the March 2013 experimental results of participating students and classes. March 1997, September 1997, March 1998, September 1998, March 1999, September 1999, March 2000, September 2000, March 2001, September 2001, March 2002, September 2002, March 2003, September 2003, March 2004, September 2004, March 2005, September 2005, March 2006, September 2006, March 2007, September 2007, March 2008, September 2008, March 2009, September 2009, March 2010 September 2010, March 2011, September 2011, March 2012, and September 2012 experimental results are also available via the WWW.


			March 2013 Experiment Summary

  School                Lat   Measured  Calculated Circumference


=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=




			September 2012 Experiment Summary

  School                Lat   Measured  Calculated Circumference

Fayetteville CC, NC[43]	35.067  85         16,430.35 km
Bennett MS, MD [18]	38.37   75	   17,533    km
Bennett MS, MD [20]	38.37   75	   20,481.6  km
Bennett MS, MD [17]	38.37   72	   21,320    km
Bennett MS, MD [16]	38.37   65	   23,616    km
Fayetteville CC, NC[9]  35.067  49.00      28,633    km
Fayetteville CC, NC[46] 37.753  47         29,846.72 km
Bennett MS, MD [15]	38.37   52	   29,520    km
Bennett MS, MD [14]	38.37   50	   30,700.8  km
Fayetteville CC, NC[41] 35.067  45         31,177    km
Commerce HS, GA [49]	34.2039	--	   31,762.5  km
Bennett MS, MD [30]	38.37   48	   31,980    km
Bennett MS, MD [13]	38.37   47	   32,660.43 km
Fayetteville CC, NC[42] 35.067  42         33,364    km
Bennett MS, MD [22]	38.37   45	   34,112    km
Commerce HS, GA [48]	34.20	56.65	   34,424.83 km / 21,390.6  mi
Fayetteville CC, NC[40] 35.067  41         34,742.93 km
Fayetteville CC, NC[47] 37.753  40         35,069.81 km
Bennett MS, MD [28]	38.37   39	   35,689.68 km
UNC Wilmington, NC	34.26   38	   36,036.20 km / 22,391.86 mi
Bennett MS, MD [23]	38.37   42	   36,548.57 km
Fayetteville CC, NC[7]  35.067  49.00      36,734.69 km
Fayetteville CC, NC[13] 35.067  38         36,906.54 km
Fayetteville CC, NC[10] 35.067  37         37,872.36 km
Fayetteville CC, NC[45] 35.067  37         37,894    km / 23,546.24 mi
Commerce HS, GA [38]	34.20	35.8377	   38,011.11 km / 23,619 mi
Fayetteville CC, NC[11] 36.067  37         38,929    km
Fayetteville CC, NC[44] 36.067  40         38,924.37 km
Fayetteville CC, NC[12] 35.067  37         38,972.10 km
Montrose School, MA	42 11	43.1	   39,186.56 km
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
Bjerget ES, Denmark[6]	57.06	57	   40,076    km
Calvary Bap Acad, LA    32.4038 32.35      40,095.21 km
Bjerget ES, Denmark[2]	57.06	56.64	   40,334    km
Bennett MS, MD [19]	38.37   38	   40,395.79 km
Commerce HS, GA [36]	34.20	33.655	   40,476.53 km / 25,150.95 mi
Nieuwen Bosch, Belgium	51.0471	50.4822527 40,478    km
Bjerget ES, Denmark[5]	57.06	56.34	   40,548    km
Del Valley Friends, PA	40 32.2	39.46	   40,647    km
Bjerget ES, Denmark[4]	57.06	56.177	   40,665.03 km
NAS Inter Col, India    28.98   28.34	   40,903.32 km
Fayetteville CC, NC[8]  37.753  37         40,919    km   
Commerce HS, GA [35]	34.2039	33.842	   40,952.38 km / 25,446.63 mi
Bjerget ES, Denmark[1]	57.06	55.77	   40,959    km
Bjerget ES, Denmark[3]	57.06	55.59	   41,093    km
Commerce HS, GA [34]	34.2039	33.14	   41,110.72 km / 25,545.02 mi
Commerce HS, GA [33]	34.203	32.4114	   42,029.32 km / 26,115.81 mi
Bennett MS, MD [25]	38.37   36	   42,640    km
Fayetteville CC, NC[32] 37.753  42         42,857    km   
James River HS, VA      37.55   37.31	   42,989.6  km
Celebration Luth, WI	44.27	41.83	   43,169    km
Bennett MS, MD [26]	38.37   35	   43,858    km
Commerce HS, GA [39]	34.2039	30.12	   44,425.13 km / 27,604.5 mi
Fayetteville CC, NC[31] 37.753  85         45,529    km   
Commerce HS, GA [37]	34.203	29.64	   45,959.14 km / 28,557.69 mi
Bennett MS, MD [29]	38.37   33	   46,520.24 km
Bennett MS, MD [27]	38.37   32	   47,970    km
Bennett MS, MD [21]	38.37   31	   49,517.41 km


[1] Solveig and Daniel
[2] Aksel
[3] Stefan and Oscar
[4] Martin and Jennie
[5] Nikolaj
[6] Plik
[7] Paula
[8] Rebecca
[9] Ashley, Paula, Lindsey, Kelly
[10] June
[11] Jane
[12] Samia
[13] Angela
[14] Ben, Peter G, Jakob K., Austin I, Sarah D.
[15] Gabriel H, Erathosthenes
[16] Ke'Ajah D, Alexis H
[17] lab 3
[18] eratosthenes experiment
[19] N. Verbits and A. Seagraves, Sarah D
[20] brandon,makai
[21] Amari
[22] Zander F, Mason O
[23] Ashley B
[24] Brooke B
[25] Anna G.
[26] patrick, Khizar Y
[27] Kaitlyn K, Courtney S, AJ Dyess
[28] Sumit S
[29] Thomas L, Chris T, Tisha C.
[30] Luke M, Ben U, Patrick T
[31] Kim
[32] Nancy
[33] Kerri, Jamal, Dillion, Francisca
[34] The COC experimentors
[35] Josh, Quay, Danielle, Chun
[36] Kyle, Qua, Tanner, Robert
[37] McClaine, Thomas, Lin
[38] Jennifer, Madison, Maria, Jake
[39] Eratosthenes
[40] Amanda
[41] Rebecca
[42] Brittney
[43] Elizabeth
[44] Bradley
[45] Desmond
[46] Kim
[47] Kathleen
[48] Holden, Tony, Trey, Megan
[49] The Docks


Boyce MS, PA
Carrollton HS, IL
Democratic School Hod Hasharon, Isreal
G S S S Alahar Yamunanagar INDIA
Gaffney HS, SC
Pine Island ES, FL
Purcell MS, OK




			March 2012 Experiment Summary

  School                Lat   Measured  Calculated Circumference

Felix Festa MS, NY[1]	41.124	60	27,438    km / 17,049.18 mi
Fayetteville CC, NC[5]	35.067  40	35,064    km / 21,787.76 mi
Felix Festa MS, NY[2]	41.124	45	36,584    km / 22,732.24 mi
James River HS, VA	37.55	40	37,575    km / 23,348.02 mi
Fayetteville CC, NC[19] 35.067  37	37,907    km / 23,554.32 mi
Fayetteville CC, NC[8]  35.067  37	37,913.5  km / 23,558.36 mi
Fayetteville CC, NC[20] 35.067  35.6	38,708    km / 24,052.04 mi
Fayetteville CC, NC[7] 111.12   36	38,960    km / 24,208.62 mi
Fayetteville CC, NC[3]	35.07   40	38,974.3  km / 24,217.51 mi
Fayetteville CC, NC[9]	35.067  35.73	39,261.13 km / 24,395.74 mi
Fayetteville CC, NC[9]	35.067  35.6	39,404    km / 24,484.51 mi
Bjerget ES, Denmark[12]	57.11	57.69	39,703    km / 24,670.30 mi
Bjerget ES, Denmark[14]	57.11	57.59	39,722    km / 24,682.11 mi
Bjerget ES, Denmark[15]	57.11	57.54	39,759    km / 24,705.10 mi
Richford Jr/Sr HS, VT   44.994  45.20	39,830.89 km / 24,749.77 mi
Bjerget ES, Denmark[13]	57.11	57.26	39,956    km / 24,827.51 mi
Fayetteville CC, NC[17]	35.07   35	40,001.14 km / 24,855.56 mi
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
Dryden HS, Canada[10]	49' 47	49.8	40,019    km / 24,866.66 mi
Fayetteville CC, NC[4]	35.07   35	40,073    km / 24,900.21 mi
Fayetteville CC, NC[6]	35.067  35	40,083.43 km / 24,906.69 mi
Dryden HS, Canada[22]	49.78	49.4	40,343.32 km / 24,866.66 mi
Dryden HS, Canada[11]	49' 47	48.544	41,054.71 km / 25,510.22 mi
Fayetteville CC, NC[18]	35.067  34	41,252    km / 25,632.81 mi
Fayetteville CC, NC[16]	35.067  33	42,501.82 km / 26,409.41 mi
Dryden HS, Canada[21]	49' 47	40	49,824    km / 20,959.20 mi


[1] Kaitlyn, Alanna, Shawna, Payton
[2] Caroline, Danielle, Josh
[3] Charles
[4] Rory, Jorge, Duwayne, Michael, Arthur, Irishmr, Clint, Ifeyinwa, Patrick
[5] Nicholas, CHZ711024, Tyler, Christopher, Dr. T Maher, James
[6] Joshua
[7] Gregory, Grenade31a, Allen
[8] Lawrence
[9] Zeus, Nakiya
[10] Michael and Lacey
[11] Adrian, Brenden, Will
[12] Jakob,Rikke, Carina
[13] Casper, Ida
[14] Emil, Markus, Jakob L
[15] Regitse, Tea, Plik
[16] Samantha, newbled1738
[17] Gerald P.
[18] Greg
[19] Justin
[20] Josh
[21] Charles
[22] Geoff, Ethan, Brittany, Jai, Kelsey, Dana


IES ITALICA, Spain
N.A.S.Inter college,Meerut,UP,India




Background:

Eratosthenes, a Greek geographer (about 276 to 194 B.C.), made a surprisingly accurate estimate of the earth's circumference. In the great library in Alexandria he read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth (sorry Columbus) by making two assumptions - that the earth is round and that the sun's rays are essentially parallel.

He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit. Eratosthenes knew from geometry that the size of the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria. Knowing also that the arc of an angle this size was 1/50 of a circle, and that the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. His result, 250,000 stadia (about 46,250 km), is quite close to modern measurements. Investigating the Earth, AGI, l970, Chapter 3, p. 66.

The formula Eratosthenes used is:

         D         A        d=distance between Syene and Alexandria
       _____  =  _____      A=360 degrees assumption of round earth
                            a=shadow angle of vertical stick
         d         a        D=to be determined (circumference)

How to Repeat the Eratosthenes Experiment Locally:

All you need to do is place a vertical stick (shaft) into the ground at your school and when the sun reaches its highest vertical ascent for the day (solar noon therefore the shadow length will be the shortest), measure the angle of the shadow of the stick (a).

                                -\
                                - \
                      stick ->  -  \
                                - a \    a=shadow angle
                                -    \
                                -     \
       ground___________________-______\shadow_______________________
Photographs of a student performing the the experiment.

Tip: Two ways to make sure the stick is in a true vertical position:

  1. Use a carpenter's level
  2. Use a rock tied to a string and dangle the rock above the ground in front of the stick
Tip: Determining solar noon for your location and time zone: By doing this experiment on the equinox we all know that the vertical rays of the sun are directly over the equator, like the well at Syene. Using a globe or an atlas, the distance between your location and the equator (d in equation) can be determined and the circumference can be calculated.
Share your results via the WWW with others around the real globe
  1. Between March 1-22, complete this on-line registration form with the following information:
  2.         Experimenter's/School's name:
            Location:
            Email address:
            School WWW address (if you have one):
            Anything else you might want to share: e.g., grade-level
  3. Between March 18-22 perform the experiment

  4. (Note: Equinox is Wednesday March 20, 2013 )
  5. Between March 20-30, complete this on-line experiment report form with the following information:
  6.         Experimenter's/School's name:
            Location:
            Email-address:
            Latitude/longitude:
            Distance to the Equator:
            Measured shadow angle in degrees:
            Calculated Earth circumference:
  7. View the experimental results of others.
  8. Try answering one or more of the Eratosthenes Experiment Bonus Questions.
Tip: If you don't know your latitude and longitude, check the Geography server at http://www.mit.edu:8001/geo. Or, you can try the newer Rutgers Geography Server: telnet geogns.rutgers.edu 3000


Graphics scans of student work from St.Stephens School, Canterbury, Kent, UK.

James D. Meinke jmeinke@youth.net

Assist. Professor of Educational Technology
Baldwin-Wallace College, Berea, Ohio

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