Eratosthenes ExperimentA Worldwide Science and Math ExperimentMarch 19, 2008

Dates to remember on this project:

·  Project Start: March 1

·  Send email that you or your class will participate: March 1-21

·  Days to measure the sun angle: March 17-21
(Note: Equinox is Wednesday, March 19, 2008 )

·  Type and post results: March 17-March 30

·  Project ends: March 30, 2008

·  Next Equinox/Eratosthenes Experiment: Monday, September 22, 2008

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--YES, IT NOW WORKS! And, we will keep the project open for an extra week so that everyone gets a chance to report their results.

You may view the March 2008 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, and September 2007 experimental results are also available via the WWW.

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

September 2007 Experiment Summary

School Lat Measured Calculated Circumference

NAS In.College,India-A 28.983 29.45 39,349.41 km / 24,450.59 mi

BG K rnerschule,AUSTRIA 48.26 48.25 39,976.78 km / 24,840.42 mi

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

Copley Homeschool, TX 29.550 29.52 40,080.21 km / 24,904.61 mi

TAPC, MO 39 38.7 40,270 km / 24,983.47 mi

Holy Family, WI 44.253 44 40,361.86 km / 25,079.7 mi

Delaware Valley FS, PA 40 02' 39.7 40,511 km / 25,117 mi

H.M. Arrndt MS, NC 35 47' 35 40,555.47 km / 25,200 mi

Silverlake MS, MA 42 25' 36 46,526.13 km / 28,910 mi

RGNV, India 30 11' 25.15 47,966.6 km / 29,805.07 mi

Athens, OH

Bjerget Efterskole, Denmark

Columbia ES, OH

Deleware Valley Friends School, PA

Evergreen JHS, UT

High Point Homeschool, NY

Humble HS, TX

Navarre, FL

Motivational Achievement Center, IL

Radnor HS, PA

Sierra Crest Academy, NV

Summit HS, WY

Zila vigyan, 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:

·  Consult your local newspaper for the sunrise/sunset times, then calculate the midpoint.

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:
  3. Location:
  4. Email address:
  5. School WWW address (if you have one):

Anything else you might want to share: e.g., grade-level

  1. Between March 17-21 perform the experiment
    (Note: Equinox is Wednesday March 19, 2008 )
  2. Between March 20-30, complete this on-line experiment report form with the following information:
  3. Experimenter's/School's name:
  4. Location:
  5. Email-address:
  6. Latitude/longitude:
  7. Distance to the Equator:
  8. Measured shadow angle in degrees:

Calculated Earth circumference:

  1. View the experimental results of others.
  2. 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: 25 October 2007

James D. Meinke


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

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