8A05.30 - Eratosthenes' Measurement of Earth's Radius

Code Number:
8A05.30
Demo Title:
Eratosthenes' Measurement of Earth's Radius
Condition:
Excellent
Principle:
Measuring the Radius of the Earth
Area of Study:
Astronomy
Equipment:
Eratosthenes' Model.
Procedure:

Place the model so that one of the pillars is pointed at the light source and gives no shadow.  Bend the cardboard and show that the other pillar produces a shadow whose size depends on the radius you have produced by bending the cardboard.

References:
  • Terrence Toepker, "A Balloon in the Sky", TPT, Vol. 61, #5, May 2023, p. 324.
  • Clinton Lewis, "A Tale of Two Bridges and a Round Earth", TPT, Vol. 60, #7, Oct. 2022, p. 614.
  • Paul Hewitt, Figuring Physics, TPT, Vol. 58, #8, Nov. 2020, p. 607.
  • Carl E. Mungan, "Sizing Up Earth with a Pair of Sticks", TPT, Vol. 57, #8, Nov. 2019, p. 516.
  • Paul G. Hewitt, "Pair-of-Sticks Hypothesis", TPT, Vol. 56, #9, Dec. 2018, p. 579. 
  • Paul Hewitt, "Solution to the September 2018 Figuring Physics", TPT, Vol. 56, #7, Oct. 2018, p. 483. 
  • "Erratum: to February 'Figuring Physics' Answer", TPT, Vol. 56, #4, Apr. 2018, p. 197.
  • Paul Hewitt, "Answer to February 2018 Figuring Physics", TPT, Vol. 56, #3, Mar. 2018, p. 160.
  • Rondo N. Jeffery, "Observing Earth From Above, Again", TPT, Vol. 52, #2, Feb. 2014, p. 69.
  • J. Mottmann, "The Size of Earth from Seven Miles Up", TPT, Vol. 51, #9, Dec. 2013, p. 555.
  • Seihi Takemae, Peter Kirwin, and Gordon McIntosh, "Reproducing Eratosthenes' Determination of Earth's Circumference on a Smaller Scale", TPT, Vol. 51, #4, Apr. 2013, p. 222.
  • Ronald A. Brown and Alok Kumar, "A New Perspective on Eratosthenes' Measurement of the Earth", TPT, Vol. 49, #7, Oct. 2011, p. 445.
  • Silvia Pugliese Jona, "Eratosthenes' Measurement", TPT, Vol. 48, #2, Feb. 2010, p. 84.
  • Dhevan Gangadharan, "Measuring the Radius of the Earth from a Mountain Top Overlooking the Ocean", TPT, Vol. 47, #8, Nov. 2009, p. 533.
  • Mark L. Biermann and Nicholas A. Nelson, "Using the GPS to Determine the Size of the Earth", TPT, Vol. 38, #6, Sept. 2000, p. 360.
  • D. Rae Carpenter, Jr., "Sight Distance at Sea", TPT, Vol. 31, #9, Dec. 1993, p. 519.
  • Zachary H. Levine, "How to Measure the Radius of the Earth on Your Beach Vacation", TPT, Vol. 31, #7, Oct. 1993, p. 440.
  • Jerry Webb and Roberta Bustin, "Eratosthenes Revisited", TPT, Vol. 26, #3, Mar. 1988, p. 154.
  • Rondo N. Jeffery and Richard G. Hills, "Eratosthenes Remembered on United Airlines Flight 456", TPT, Vol. 25, #8, Nov. 1987, p. 500.
  • Kevin Krisciunas et al., "The First Three Rungs of the Cosmological Distance Ladder", AJP, Vol. 80, #5, May 2012, p. 429.
  • Frank O. Goodman, "Measure the Earth's Radius While Boating on One of its Lakes", AJP, Vol. 61, #4, Apr. 1993, p. 378.
  • Dennis Rawlins, "Doubling your Sunsets or How Anyone Can Measure the Earth's Size with Wristwatch and Meterstick", AJP, Vol. 47, #2, Feb. 1979, p. 126.
  • Jearl Walker, "The Amateur Scientist: How to Measure the Size of the Earth with Only a Foot Rule or a Stopwatch", Scientific American, Vol. 240, #5, May 1979, p. 172.
  • "S-360. Sight Distance at Sea", DICK and RAE Physics Demo Notebook, 1993.
  • Christopher P. Jargodzki and Franklin Potter, "359, Measuring the Earth", Mad About Physics, p. 141, 282 - 283.
  • Jim Glenn, "The Geometers", Scientific Genius: The Twenty Greatest Minds, p. 18 - 19.
  • Robert P. Crease, "Measuring the World: Eratosthenes' Measurement of the Earth's Circumference", The Prism and the Pendulum, p. 2.

Disclaimer: These demonstrations are provided only for illustrative use by persons affiliated with The University of Iowa and only under the direction of a trained instructor or physicist.  The University of Iowa is not responsible for demonstrations performed by those using their own equipment or who choose to use this reference material for their own purpose.  The demonstrations included here are within the public domain and can be found in materials contained in libraries, bookstores, and through electronic sources.  Performing all or any portion of any of these demonstrations, with or without revisions not depicted here entails inherent risks.  These risks include, without limitation, bodily injury (and possibly death), including risks to health that may be temporary or permanent and that may exacerbate a pre-existing medical condition; and property loss or damage.  Anyone performing any part of these demonstrations, even with revisions, knowingly and voluntarily assumes all risks associated with them.