Name_____________________________________ Date __________ Measuring the Earth
One of the most important things to know about the Earth is its size and shape. Many of Earth’s important properties are a result of its size, but how can you measure this giant rock we all are standing on. Many ancient peoples knew that the Earth is spherical in shape. The first recorded measurement of the Earth was by Eratosthenes--head librarian at Alexandria, Egypt. He made very accurate measurements of the angle that the sun’s shadow made at two points on the surface of the Earth (in this case Alexandria and Syene--more than 500 miles apart). We will repeat Eratosthenes’ experiment using the sun’s shadow as well as GPS receivers over a long distance (not quite 500 miles though) as well as a short one.
At the first stop: measure the length of the shadow cast by your measuring device. Using inverse tangent of height / shadow length, calculate the sun’s shadow’s angle. This should be your latitude (if measured on the equinox). Record this number. Then use the GPS system to get your latitude. Record this number too. Are they the same? If not, why not?
We will then climb back into the cars. Set the trip log on the car’s odometer so we can figure out how far we are traveling. Record the distance traveled. At the other stop: repeat the procedure above to get the latitude for this stop. Record the shadow angle and the GPS recording.
Find the difference between the two angles. With this number, you can simply calculate the circumference of the Earth by setting up the following equation: angle diff. / 360 = dist. / circ. Calculate the circumference of the Earth.
Do this for both your GPS angles as well as your shadow angles.
Back at Riverside, you will repeat this whole activity (just the GPS part) with two points only a short walk apart. What are the two latitudes and your distance? What is your calculated circumference?
Eratosthenes obtained a circumference of 40,000 km.
How do the three of your calculations of the circumference (shadow, GPS-car, and GPS-walk) compare with each other, with Eratosthenes value, and to the accepted value?
Using your most accurate readings: calculate your % error
% error = (difference between accepted and your / accepted) x 100
What do you believe was your biggest source of error in each trial?