# Eratosthenes Activity

```Information in Radio Waves
Name: ________________________________ Class: ___________
Date: ___________
Recreating Eratosthenes’ Experiment
Introduction:
Eratosthenes (276 - 195 B.C.) was a man of many
trades. He was a mathematician, geographer, poet,
astronomer, and even a music theorist. Throughout
his life he made many contributions and many more
attempts at others. Included in this list is his
invention the armillary sphere, used to model
celestial objects in the sky, and the mathematical
model known as the Sieve of Eratosthenes (for
finding prime numbers). His most important
contributions were to astronomy and geodesy
though.
Eratosthenes is credited with the first remarkably accurate measurement of both Earth’s
circumference as well as Earth’s radius. How did he do it? To be frank, he did it by using a
camel, the sun, and a lot of assumptions; not the typical methodology of a successful
experiment. Surprisingly it all worked out, achieving an accuracy of at least 16% to today’s
numbers. Depending on which stadion is used though (the stadion was the system of
measurement at the time), Eratosthenes may have achieved numbers within 2%.
Your job? Recreate Eratosthenes methods and achieve even better numbers.
Materials:
- computer with an internet connection
- calculator (if needed)
Methods:
Step 2 - Go to your home town and mark that location. Find a second location that is
approximately 925 km directly north or south from your hometown and in the same
hemisphere. Make note of what you chose. If this isn’t possible for your location, use Chicago,
IL and Tuscaloosa, AL.
Step 3 - Open up a new tab and go to http://aa.usno.navy.mil/data/docs/RS_OneDay.php.
Determine the local noon on June 21 for either your hometown or for Chicago.
Step 4 - Now determine the angle at which the sun strikes both cities during the summer
solstice. To do this, use the following method:
During the summer solstice the Sun is directly over the latitude 23.5⁰N. There the sun
will be striking at the maximum 90⁰. By determining the latitudes of both locations, you
can calculate the angle the sun is in the sky at noon. For example:
At a location 32⁰N: 90⁰ - 32⁰ + 23.5⁰ = 81.5⁰
Step 5 - Calculate the difference in angles for both cities. If we assume the Earth to be a perfect
sphere, how much of the Earth lies between your two points (how many degrees out of 360)?
Step 6 - Using this website: http://www.freemaptools.com/how-far-is-it-between.htm find the
exact distance between your two locations. Using this number and the results you got from step
5, calculate your circumference of Earth.
Step 7 - From the circumference, calculate the radius. (C = 2𝜋𝑟)
First Location: _________________
Latitude:
Second Location:________________
________
________
Time of noon: ________
________
Angle of sun at noon for Location 1:
Angle of sun at noon for Location 2:
Difference in angle: _________
Distance between locations: _________
Finding the Circumference:
difference in angle = distance between locations
360⁰
C
Circumference: _______________
Discussion Questions:
1.) Convert your calculations of circumference and radius from km to miles (1 km = 0.62 miles).
2.) Why would it be important to know when the local noon occurs? Think about before google
maps and modern cartography existed.
3.) In the example given for calculating the angle of the sun, what does each part represent?
Why does each have to be there for the calculation to work?
4.) What was your percent error for your circumference calculation? What are the sources of
error for this experiment? Compare yours to that of Eratosthenes.
```