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 2012
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, and
September 2011
experimental results are also available via the WWW.
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 September 2011 Experiment Summary School Lat Measured Calculated Circumference Cole Ridge HS, CO[38] 39 37 74 21,381.1 km / 13,285.6 mi Fayetteville TCC,NC[30] 35.07 45 31,117.03 km / 19,335.23 mi Fayetteville TCC,NC[9] 35.07 45 31,118.08 km / 19,335.88 mi Fayetteville TCC,NC[10] 35.07 45 31,142.16 km / 19,350.84 mi Fayetteville TCC,NC[3] 35.07 45 31,173.6 km / 19,370.38 mi Fayetteville TCC,NC[8] 35.07 45 31,173.6 km / 19,370.38 mi Fayetteville TCC,NC[13] 35.07 45 31,173.6 km / 19,370.38 mi Fayetteville TCC,NC[17] 35.07 45 31,173.6 km / 19,370.38 mi UNC Wilmington, NC 34.23 37 37,298.50 km / 23,176.22 mi Cole Ridge HS, CO[34] 39 37 48.36 37,997 km / 23,610.24 mi Cole Ridge HS, CO[24] 39 37 41.5 38,125 km / 23,689.78 mi Belle Vernon HS, PA 40.18 42 38,274.17 km / 23,782.47 mi Dryden HS, Canada[21] 49.78 51.78 38,656.11 km / 24,019.79 mi Fayetteville TCC,NC[1] 35.07 30 38,724 km / 24,061.98 mi Fayetteville TCC,NC[6] 35.07 30 38,924.72 km / 24,186.7 mi East HS, MO [15] 39 6 51.9 39,000 km / 24,233.48 mi Cole Ridge HS, CO[25] 39 33 40.39 39,173 km / 24,340.98 mi East HS, MO [19] 39 6 50 39,200 km / 24,357.75 mi Cole Ridge HS, CO[35] 39 33 40.2 39,358 km / 24,455.93 mi Harry M Arndt MS, NC 35 46 36 39,600.64 km / 24,606.7 mi Cole Ridge HS, CO[28] 39 33 39.66 39,894 km / 24,788.98 mi Fayetteville TCC,NC[5] 35.07 45 39,960 km / 24,829.99 mi Riverbend Academy, FL 29.251 29 39,981.85 km / 24,843.57 mi =>Earth's Polar Circumference 40,008 km / 24,859.82 mi<= Fayetteville TCC,NC[16] 35.07 45 40,010.98 km / 24,861.67 mi Cole Ridge HS, CO[27] 39 33 39.54 40,015.51 km / 24,864.49 mi Cole Ridge HS, CO[29] 39 33 39.54 40,034 km / 24,875.98 mi Fayetteville TCC,NC[2] 35.07 35 40,036.8 km / 24,877.72 mi Fayetteville TCC,NC[11] 35.07 35 40,114.3 km / 24,925.87 mi Galesburg HS, IL 40.94 40 40,500 km / 25,165.53 mi Cole Ridge HS, CO[36] 39 33 39.05 40,517.29 km / 25,176.28 mi Fayetteville TCC,NC[4] 35.07 34.5 40,617.03 km / 25,238.25 mi Pine Island ES, FL 26 37 26 40,734.10 km / 25,311 mi Fayetteville TCC,NC[12] 35.07 42 40,834.29 km / 25,373.25 mi Bjerget ES, Denmark 57.06 55.9 40,860 km / 25,389.23 mi Cole Ridge HS, CO[26] 39 33 38.7 40,883.7 km / 25,403.95 mi East HS, MO [14] 39 6 51.9 40,900 km / 25,414.08 mi East HS, MO [18] 39 6 52 41,200 km / 25,600.49 mi Cole Ridge HS, CO[33] 39 33 33.7 41,582.4 km / 25,838.11 mi East HS, MO [20] 39 6 52 41,900 km / 26,035.45 mi Cole Ridge HS, CO[32] 39 33 37.73 41,930 km / 26,054.1 mi Howell HS, NJ 40.2 40 41,958 km / 26,071.49 mi Cole Ridge HS, CO[31] 39 33 37.45 42,248.33 km / 26,251.9 mi Cole Ridge HS, CO[39] 39 33 37 42,762 km / 26,571.08 mi Cole Ridge HS, CO[37] 39 33 37 43,229.50 km / 26,861.57 mi Fayetteville TCC,NC[7] 35.07 32 43,790.06 km / 27,209.88 mi Dryden HS, Canada[22] 49.78 39.6 53,450 km / 33,212.29 mi [1] Veronica [2] Patricia [3] Tovey C - Bad equator distance: 9002 km; recalculated using 3896.7 km [4] Lindsay, Tara [5] Wanda [6] Marcella [7] Emma, Lashunda, Eratosthenes [8] Roosevelt - Bad equator distance: 9528 km; recalculated using 3896.7 km [9] Sherlene [10] Mandy [11] Lauran [12] Shani [13] Angela - Bad equator distance: 38,924.649 km; recalculated using 3896.7 km [14] Team blue [15] Team AAAS [16] Amy [17] Tammy - Bad equator distance: 9002 km; recalculated using 3896.7 km [18] Team 1 [19] Team 2 [20] Team 3 [21] Alex, Caine, Ethan, Ryan [22] Marion, Kara, Mark, Phil [23] #1 [24] tuyet [25] team [26] Team Legit [27] Team We Tried [28] Los Frijoles [29] Team Name [30] Roosevelt [31] XXL's [32] BF Changs [33] Harvey's [34] The Greek Wannabe's [35] Awesomesauce on 27 [36] OliviannAustinators [37] BAMF's [38] What [39] Barbies AGS - Alssundgymnasiet Snderborg, Denmark Central HS District of Westosha, WI Frewsburg Central HS, NY Grace Christian Academy, Taiwan Highland HS, AR The Planetary Society/FaCE CA Turkeyfoot Valley HS, PA Warwick Valley HS, NY March 2011 Experiment Summary School Lat Measured Calculated Circumference Parkwood MS, NC 34.8979 45 31,077.54 km / 19,310.69 mi FICC, NC[12] 36.07 44.0 31,877.50 km / 19,807.76 mi Cole Ridge HS, CO[17] 39.55 46.8 33,869.00 km / 21,045.22 mi FICC, NC[10] 36.07 40.0 35,013.00 km / 21,756.07 mi FICC, NC[5] 36.07 39.0 36,034.09 km / 22,390.55 mi Cole Ridge HS, CO[20] 39.55 41.82 37,902.00 km / 23,551.21 mi Cole Ridge HS, CO[18] 39.55 41.6 38,102.80 km / 23,675.98 mi Bjerget ES, DENMARK[1] 57 06' 58.5 39,068.00 km / 24,275.73 mi Bjerget ES, DENMARK[2] 57 06' 58.3 39,181.00 km / 24,345.95 mi Cole Ridge HS, CO[14] 39.55 39.55 39,250.00 km / 24,388.82 mi Bjerget ES, DENMARK[3] 57 06' 57.9 39,442.00 km / 24,508.12 mi Cole Ridge HS, CO[19] 39.55 40.035 39,592.16 km / 24,601.43 mi FICC, NC[8] 36.07 40.0 39,633.24 km / 24,626.95 mi Cole Ridge HS, CO[25] 39.55 39.8 39,844.20 km / 24,758.04 mi APerbosc College,FRANCE 44 08' 44 16' 39,882.00 km / 24,781.53 mi =>Earth's Polar Circumference 40,008 km / 24,859.82 mi<= W Essex HS, NJ 41 -- -- / -- ** FICC, NC[7] 36.07 38.0 40,009.00 km / 24,860.44 mi Cole Ridge HS, CO[21] 39.55 40.183 40,027.27 km / 24,871.79 mi Cole Ridge HS, CO[15] 39.55 50.2 40,074.27 km / 24,901.00 mi FICC, NC[13] 36.07 35.0 40,076.00 km / 24,902.07 mi Cole Ridge HS, CO[24] 39.55 39.47 40,149.00 km / 24,947.43 mi IntSchool Paris, France 48 49' 48 40,688.69 km / 25,282.78 mi* Bjerget ES, DENMARK[4] 57 06' 56 40,786.00 km / 25,343.25 mi Cole Ridge HS, CO[22] 39.55 38.7 40,905.00 km / 25,417.19 mi FICC, NC[9] 36.07 34.0 41,333.00 km / 25,683.14 mi Cole Ridge HS, CO[16] 39.55 36.625 42,617.82 km / 26,481.49 mi Cole Ridge HS, CO[23] 39.55 36.82 43,049.43 km / 26,749.68 mi *Corrected latitude and distance to Equator **Unable to complete experiment because of cloud cover Bjerget ES, DENMARK[1] - Kasper Bjerget ES, DENMARK[2] - Plik Bjerget ES, DENMARK[3] - Annika og Sebastian Bjerget ES, DENMARK[4] - Joachim FICC, NC[5] - Jeremy, Brook, Felton, Ronnie FICC, NC[6] - Michael Bad angle/ Equator distance FICC, NC[7] - Jackie, William FICC, NC[8] - David FICC, NC[9] - Robert, Henry FICC, NC[10] - Briana FICC, NC[11] - Melissa Not at solar noon FICC, NC[12] - Ernest, Roland, David FICC, NC[13] - Derek Cole Ridge HS, CO[14] - Powderpuff Girls, AA Participants Cole Ridge HS, CO[15] - Fantastic Four Cole Ridge HS, CO[16] - Michael, The Shockers Cole Ridge HS, CO[17] - The Avengers Cole Ridge HS, CO[18] - CACK Cole Ridge HS, CO[19] - John, Sami, Lena, Kathleen, Kelvin Cole Ridge HS, CO[20] - McLovin Cole Ridge HS, CO[21] - ATTWF Cole Ridge HS, CO[22] - NoNames Cole Ridge HS, CO[23] - Ty, Trevor, Zoe, Si, Alicia Cole Ridge HS, CO[24] - Kinsey, Cameron, Zach, Snoder Cole Ridge HS, CO[25] - Chelsie, Jessica, Brini, Amanda Bay Point MS, FL Caterham, UK Felix Festa MS, NY IIS-S "G. La Pira", Italy Int School Dhaka, Bangladesh NEMiles Jewish DS, AL Madison MS, NM Northwest MS, TN NYC iSchool, NY Waples Mill ES, VA Swan River Montessori Charter School, MNBackground:
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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