Module 2: How We Know What We Know

ERATOSTHENE'S SHADOW


Overview: Measure the length of a shadow at solar noon. Using your measurement and those from others in the class, plus a map, calculate the circumference of Earth. Below are more detailed instructions, with questions to consider. You may use them, vary them, or devise your own experiment to accomplish the same goal. The questions are to guide you, not to answer specifically.

 

1. Choose a day to measure shadows. Notes: I suggest using the first Saturday of the module as the target date, but make a measurement as soon as you can, because it may be cloudy on the target date. Is it important for everyone to have measurements on the same day? If not, how many days apart is acceptable?

2. Measure the height of a vertical object. Measure the length of the shadow cast by that object at solar noon.

Notes: It's very important that you know the vertical height of the object. The easiest way to do this is to use a meter stick to cast the shadow, making sure that it's truly vertical. Either use a plumb line and fix the meter stick in place, or have someone hold it steadily vertical. A taller object, assuming you can measure it accurately and the shadow is really horizontal, will give you a more accurate measurement. Tape or tie a crosspiece (stick, pencil, whatever) to a flagpole at the height of 2 meters, for example. Mathematicians: why does this matter? Also, it's important to get the measurement at solar noon. How will you figure out when it is solar noon? (Suggestion: you can do it experimentally by tracking the shadow for half an hour or more near solar noon. When the length of the shadow starts changing in the other direction, you've passed noon. The graphically-oriented can take many measurements, plot them, and determine a very precise shadow length.)

3. Report your measurements: date, time (by the clock), object height, shadow length, and your location.

4. In teams, use the measurments taken by course participants to calculate the circumference of Earth. You will need to use a map to measure the distance between you. Repeat this with the measurements from a third participant. (The mathematically-inclined may wish to get a statistical value and uncertainty.) There are on-line maps and distance calculators for those who wish to make use of them.

Notes: Is it important that the other person makes the measurement at the same time as yours? Eratosthenes used two places on a north-south line. Is this necessary? If not, what can you do to compensate for the east-west distance?

5. Post your measurements to the appropriate folder in the Module 2 conference as soon as possible for group discussion and calculations.

6. Individually, turn in your measurements and a summary of how you used this data to find the Earth's size to the homework folder. Note any problems or difficulties and lessons learned. How would you improve the experiment if you were to do it again?

7. As a team, turn in the final calculations and results to the homework folder.

Note: Check out:

Eratosthenes's Shadow and this Cooperative Activity


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Montana State University

last updated 2/3/02