VI. Measuring the Size of the Earth

1. If you are going to be traveling 150 miles or more due north or south this semester (the farther the better), you can measure the size of the Earth. The two observations needed should be done at about the same time of night within about a week or two of each other. (This is because Polaris really does move a small amount.) The measurements of this project can give surprisingly good results for the size of the Earth, but you must be very careful in measuring angles (below).
2. Tape a soda straw firmly to a piece of cardboard. On a clear night at the northernmost location, hold the cardboard vertically and sight Polaris (the North Star) through the straw. Now, without moving the cardboard, draw a vertical line on the cardboard. This may be most easily done by hanging a small weight (such as a stone) from a string. (An assistant helps here too!) Hold the string up along the cardboard, and then draw a line with a ruler lined up along the string.
3. Do the same thing at the southernmost location using the same piece of cardboard. You should have two vertical lines that cross at a small angle. Record which line is which, and be sure to record the date, time, and location for each measurement. (See the instructor for any clarifications regarding this procedure.)  When you turn in your project, include the cardboard-string-washer device, along with the lines and notes you drew on it.                                                      
4. Record the north-south distance between your two observing locations. The north-south distance should be measured using a map. This will be less than your actual travel distance, unless you traveled straight north or south. 
5. Using a protractor, measure the angle between the two vertical lines. (The lines cross because the direction of “vertical” — measured relative to the stars — has changed as you moved around the Earth’s surface. The angle between the lines is the number of degrees of latitude that you have moved.) Divide 360 degrees by the number of degrees between the two vertical lines and multiply the result by the north-south distance between the two locations where you made your observations. Your answer should be close to the circumference (the distance around) of the Earth.
6. Look up the circumference of the Earth in your textbook; or, calculate it from looking up the radius or diameter of the Earth.  (Be careful!  Remember that the circumference is the distance around the Earth, while the diameter is the total distance through the center of the Earth, and the radius is half the diameter.)  How well does your answer agree with this value?  Explain how well your answer agrees and why.