Information in Radio Waves

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 1 - Open up Google Maps on your web browser.

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)

Answers Section:

First Location: ______Second Location:______

Latitude: ______

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: ______

Radius: ______

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.