Name_____________________________________ Date __________ Measuring the Earth
Eratosthenes Lab.
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 over a long distance (not quite 500 miles though) as well as a short one.
First we will do this walking on campus. Choose the route of our measurements. Directly north - south and as level as possible will decrease our errors. Now, at one end, using GPS coordinates record the latitude (shadow angle if measured at noon on the equinox). Measure the distance between the two locations. Using the GPS coordinates at the other end of our route, record the latitude. Using the following formula, calculate the circumference of the Earth:
angle difference / angles around a sphere = distance walked / circumference.
The angle difference is the difference between the latitudes (subtract the smaller one from the bigger one)
The number of angles around a sphere is 360 x 60 (since we measured in minutes and there are 60 minutes in a degree and 360 degrees in a sphere)
What is your calculated circumference?
What do you believe is your biggest source of error?
Now we are going to scale this up and try over a larger distance. We will plan out a route to drive. We will also do this with shadows as well.
At the first stop: measure the shadow 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?
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 between the two spots.
At the second 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.
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?
What do you believe was your biggest source of error in each trial?