Celebrate Earth Day Measure the Size of the Earth
About 240 BC (over 2,200 years ago), Eratosthenes (chief of the library in Alexandria - one of the greatest libraries of the ancient world) measured the circumference of the Earth.
On the day of the summer solstice, he noted that the Sun stood directly above the city of Syene (now Aswan) in Egypt. On the same day, 800 km to the north, the Sun cast a shadow equal to 1/50 of a circle (7.2 o ) in Alexandria. We invite you to use these measurements (and your own measurement) to measure the circumference of the Earth on Earth Day.
Use a meter stick (or a yard stick). Find a level surface out in the sun. Hold the stick vertical with the bottom touching the ground. Use a plumb line or a bubble level (spirit level) to keep your stick vertical
Measure and record the length of the shadow the stick casts every 10 minutes from 11 o’clock to 1 o’clock (your local time). If Earth Day is cloudy, you may measure the shadow on any sunny day within a week of Earth Day.
On graph paper, plot the times and the shadow lengths: “ 11” = 11 o’clock; “11.5” = 11:30 Length (cm) Local Time
Draw or compute the best curve through your data points. Find the lowest point of the curve (your shortest shadow length). Divide (shadow length/stick length) In the graph shown, the shortest shadow length is 35.6 cm, so 35.6 cm/100 cm = 0.356 Find the angle whose tangent is your answer. In our example, tan(X) = 0.356 X = arctan(0.356) = tan -1 (0.356) X = 19.6 o The Sun angle is 19.6 o
Choose any other city and their angle (in your hemisphere - north or south) (for this example, say I choose a city with an angle of 39.6 o ) Take the bigger angle and subtract the smaller angle. (39.6 o - 19.6 0 = 20.0 o ) Calculate the latitudinal (north-south) distance between your two cities using Eratosthenes’ original measurements: your angle difference equals 7.2 o your distance 800 km In this example: 20.0 o equals 7.2 o X km 800 km and X = 2200 km (the latitudinal distance)
When you have your latitudinal distance, divide it by your angle difference In our example: 2200 km/20.0 o = 110 km/degree Now multiply your distance by 360 degrees In our example: (110 km/degree) times (360 degrees) = 39,600 km Congratulations - you have measured the Earth’s circumference Upload your measurement of the circumference of the Earth. Thank you for recreating this classic experiment for Earth Day.
Dr. Robert Cassidy SUNY Ulster County Community College [email_address]