Eratosthenes Experiment
A Worldwide Science and Math Experiment
March 20, 2009

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 2009 experimental results of participating students and classes. March 1997, March 1997, March 1998, March 1998, March 1999, March 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, and September 2008 experimental results are also available via the WWW.



		     March 2009 Experiment Summary

  School                Lat   Measured  Calculated Circumference

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





		     September 2008 Experiment Summary

  School                Lat   Measured  Calculated Circumference

Coal Ridge HS, CO[20]	39     219.029	31,652.64 km / 19,668.04 mi
Lale Youth IS, Maldives	 4 13'	 5	33,780    km / 20,989.92 mi
West HS, IA [9]		42.5	47.5	36,522.6  km / 22,694.09 mi
St. George's IS, TN	35.162	37.5	37,445.91 km / 23,267.81 mi
Valley ES/MS, PA	40 59'	43.5	37,665.08 km / 23,404    mi
UNC Wilmington, NC	34.3	37.7	37,712.43 km / 23,433.42 mi
Pine Island ES, FL	26 37'	27.9	37,959.59 km / 23,587    mi
West HS, IA [6]		42.5	45.3	37,993.22 km / 23,607.89 mi
Coal Ridge HS, CO[18]	39 33'	90	38,227.8  km / 23,753.65 mi
West HS, IA [7]		42.5	51	38,823.5  km / 24,123.81 mi
Coal Ridge HS, CO[21]	39	40.3	38,885.31 km / 24,162.21 mi
FISH Homeschool Coop,Jp	26 20'	27	39,108    km / 24,300.59 mi
Coal Ridge HS, CO[14]	39.57	40.17	39,398.36 km / 24,481.01 mi
West HS, IA [5]		42.5	43	39,495.34 km / 24,541.27 mi
HSGroup w/ Sunfield, WA	47	48	39,601.93 km / 24,607.5  mi
Del Val Friends Schl,PA	40 02'	40.40	39,655    km / 24,640.48 mi
Brown Home School, CA	39.81	40	39,816.78 km / 24,741    mi
Combe Bank Schl, Uk[10]	51.282	51.239	39,853.06 km / 24,763.54 mi
Magnetic Island SS, Au  19 08'	19.2	39,864.1  km / 24,770.40 mi
OD Christian Academy,PA	40.155	40.1265	39,894.03 km / 24,789    mi
Heights-Terrace ESMS,PA	40 57'	40.5	39,905.29 km / 24,796    mi
Liceo Scientifico, It	45 35'	45.5	39,911    km / 24,799.54 mi
Combe Bank Schl, Uk[11]	51.282	51.239	39,932    km / 24,812.60 mi
Koc MS, Istanbul, Tr	40 55'	40.7	39,980    km / 24,842.42 mi
Fort Hamilton HS, NY	42.6	42.6	39,996    km / 24,852.36 mi
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
Drums ES/MS, PA		41 00'	41	40,074.27 km / 24,901    mi
Coal Ridge HS, CO[16]	39.57	39 33'	40,093.34 km / 24,912.85 mi
A. Perbosc Col, Fr	44 08'	44	40,115    km / 24,926.31 mi
Bjerget Efterskole, Dk	57 06'	59.92	40,133.87 km / 24,938.03 mi
Clearview MS, NJ	39.45	39.6	40,160.37 km / 24,954.5  mi
Fallston HS, MD		39.5219	39.007	40,528    km / 25,182.93 mi
N.A.S.Inter Col, In[1]	29.098	20.532	40,766.85 km / 25,331.35 mi
Coal Ridge HS, CO[13]	39 33'	38.72	40,873.76 km / 25,397.78 mi
N.A.S.Inter Col, In[3]	29.083	28.387	40,975    km / 25,460.69 mi
Coal Ridge HS, CO[19]	39	90	41,648.21 km / 25,878.00 mi
West HS, IA [8]		42.5	47.5	41,684.2  km / 25,901.36 mi
West HS, IA [12]	42.5	44.7	41,684.2  km / 25,901.36 mi
N.A.S.Inter Col, In[4]	29.083	27.41	42,435    km / 26,367.89 mi
Coal Ridge HS, CO[17]	39.5	37 22'	42,521    km / 26,421.33 mi
N.A.S.Inter Col, In[2]	29.083	27.15	42,841.99 km / 26,620.78 mi
Dutchtown HS, LA	30 13	28	44,060.62 km / 27,378    mi
Coal Ridge HS, CO[15]	39.57	90     251,416.62 km /156,223.05 mi


[1]  Group 1
[2]  Group 2
[3]  Group 3
[4]  Group 4
[5]  Franco, Brendan
[6]  Javan, Connor, Jordan, Trevor
[7]  Alec, Kristina
[8]  Sehrizad, Austin
[9]  Joseph, Brent
[10] Katie
[11] Eloise, Alice
[12] Abby, Abby
[13] Alto
[14] Dillon, Drew, Crockett, Andy
[15] Group 15
[16] Group 16
[17] Group 17
[18] Group 18
[19] Group 19
[20] Group 20
[21] Group 21


Akshara Vidyaashram, In
Alice Vail, AZ
Ankori, Is
Colegio Pedro Poveda, Sp
E. LaFontaine, Fr
Eton School, WA
Freeland EMS, PA
Friends School of Portland, ME
Hazleton EMS, PA
Hebrew USS, Il
Hopewell Academy, NC
HM Arndt MS, NC
Koinonia, GA
Madras Col., Uk
McCall HS, ID
North Carolina State University, NC
NW Mississippi CC, MS
Orange Ave ES, CT
Peakirk cum Glinton, Uk
West Hazleton EMS, PA
Wyoming Valley West MS, PA


		     March 2008 Experiment Summary

  School                Lat   Measured  Calculated Circumference


NASI College, In[8]	29.083	29.6	39,262.05 km / 24,396.31 mi
Eldridge FHS, WA	47 20'	48	39,336.39 km / 24,442.5  mi
NASI College, In[5]	28.983	29.2	39,663.34 km / 24,645.66 mi
HAAC, Vn[1]		10.03	 9.74	39,773    km / 24,713.80 mi
Pittsfield MS/HS, NH	43.32	43.8	39,800.68 km / 24,731    mi
College Perbosc, Fr	44 08'	44.128	40,007    km / 24,859.20 mi
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
UWG Adv Academy, GA	33.537	33.4	40,009.6  km / 24,865.29 mi
Richford Jr/Sr HS, VT	45 00'	45.662	40,011    km / 24,861.68 mi
Kaisiadorys SS, Li	54 51'	54.7	40,027.78 km / 24,872.11 mi
Ecole Lafontaine,Fr	50 17'	50.184	40,079    km / 24,903.94 mi
NASI College, In[6]	28.983	28.89	40,088.64 km / 24,909.93 mi
HAAC, Vn[2]		19.28	19.24	40,031.70 km / 24,874.55 mi
Tinh Gia 1 HS, Vn	19 28'	19.4528	40,031.72 km / 24,874.56 mi
NASI College, In[7]	28.983	28.83	40,172.06 km / 24,961.76 mi
HAAC, Vn[3]		13.95	14.75	40,271    km / 25,023.24 mi
Koinonia Cntr, GA	33 44'	33.46	40,309.7  km / 25,047.29 mi
Bates Academy, NH	42 48	41.9	40,898.26 km / 25,413    mi
Corder FHS, NC		35 16'	34	41,295.76 km / 25,660    mi
Woodside Park IS, Uk	51 48'	50	41,407    km / 25,729.12 mi
NASI College, In[4]	28.983	29.9	42,942    km / 26,682.92 mi

[1] CanTho
[2] TinhGia - Ngo
[3] Pleiku - Tan
[4] Deepak
[5] Mahender
[6] Rakesh
[7] Depak
[8] Depak


Antonin Perbosc, Fr
D.H.I. College, In
Galvin MS, MA
A.S.I. College, In
Peninsula HS, WA
S.I. College, In
Zila V. Club, 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 18-23 perform the experiment

  4. (Note: Equinox is Friday March 20, 2009 )
  5. Between March 19-30, 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.
Last modified: 12 November 2008
James D. Meinke jmeinke@youth.net

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

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