>>7068640http://www.msnbc.com/rachel-maddow-show/eratosthenes-shadow1) Calculate the angle the sun’s rays hit your stick at solar noon using the equation given below. You and your friend should each do this separately. This will give you TWO ANGLES, one for the person at the higher latitude location and one for the person at the lower latitude location. [Hint: the function below is called “arctan” and appears on any scientific calculator.]
2) Whichever one of you has the smaller angle, subtract this from the bigger one. This is your THETA.
3) Find the distance in miles or kilometers between the LATITUDE of your location and the LATITUDE of your friend’s location. (DO NOT find the distance as the crow flies.) This is your DISTANCE.
4) Now for the grand finale! Your THETA represents a portion of a full circle, a fraction of 360 degrees. Your DISTANCE is the equivalent fraction of the Earth’s circumference. So divide 360 by your THETA and multiply by your DISTANCE. TA-DA! You’ve calculated the circumference of the Earth. [Note: your circumference will be in the same units as your stick and shadow so a little unit conversion may be in order.]
