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 September 2009
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, and
March 2009
experimental results are also available via the WWW.
September 2009 Experiment Summary School Lat Measured Calculated Circumference =>Earth's Polar Circumference 40,008 km / 24,859.82 mi<= Howell HS, NJ March 2009 Experiment Summary School Lat Measured Calculated Circumference Bentworth S HS, PA 40.125 40.96 39,009.60 km / 24,239.44 mi M Thornton ES, NH 42.850 43 39,928.94 km / 24,810.78 mi Safalta Int Col, India 29.056 29.1 39,939.67 km / 24,817.36 mi Richford JRSR HS, VT(2) 44.9945 45.047 39,961 km / 24,830.62 mi =>Earth's Polar Circumference 40,008 km / 24,859.82 mi<= Bjerget Efters, Denmark 57 06' 57.08 40,021.71 km / 24,868.34 mi N Londonderry, NH 42.5505 42 40,121.23 km / 24,930.26 mi Richford JRSR HS, VT(1) 44.9945 44.732 40,243 km / 25,005.84 mi Saetbyeol MS, S Korea 37 26' 37 40,514 km / 25,174.23 mi N.A.S.Inter Col, India 28.933 28.4 40,740.46 km / 25,321.16 mi Brocton Central, NY 42 23' 41 41,382.4 km / 25,713.83 mi Fallston HS, MD 39.52 Cloudy/no shadow on Equinox-Raining on next attempt Arcadia MS, WI Bjerget Efterskole, Denmark (2) Brown HS, CA La Nuova Scuola, Italy Lifeforte, Nigeria Mt Vernon HS, TX Univ Lab School, HI Wausaukee ES, WI 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, PABackground:
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)
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:
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
Experimenter's/School's name:
Location:
Email-address:
Latitude/longitude:
Distance to the Equator:
Measured shadow angle in degrees:
Calculated Earth circumference:
James D. Meinke jmeinke@youth.net
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