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,IndiaBackground:
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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