The Eratosthenes Measurement
Information about the position of the Sun, especially its altitude above the horizon can be used to determine the circumference of the Earth - an exercise that was done by Eratosthenes, a Greek Philosopher and Mathematician. Living about 2 000 years ago Eratosthenes was in charge of the Library at Alexandria. He had read that on a certain date the Sun would be directly overhead in Syene a city to the south of Alexandria. This interested him as on that same date the Sun was not directly overhead in Alexandria, but was about 7 degrees less.
Eratosthenes reasoned that 7 degrees was about 1/50th of a complete circle (360 degrees) and that this would represent the angular distance between Syene and his home city of Alexandria. Eratosthenes also knew the ground distance between the two cities. Assuming that the difference between the two angles is to 360 degrees as the ground distance is to the Earth's circumference, Eratosthenes multiplied the ground distance by 50 and came up with a figure for the Earth's circumference that was very close to the actual circumference.
The typical Eratosthenes measurement project is done by linking with another location on the same longitude but at a different latitude. For SunShIP all locations will make a direct (straight line) measurement, north or south, between the equator (0 degrees latitude) and their own local latitude for the distance measurement.
The activity is simply done by measuring the mid-day altitude angle of the Sun locally and then comparing that with the mid-day altitude angle at the equator and subtracting the two to determine the altitude angle difference.
The surface distance between the local observing location and the equator in kilometers will need to be determined as well (1 degree equals 110.2 km).
Then using the following formula the circumference of the Earth can be calculated.
Earth's Circumference = distance in kilometers from the equator * (360/angle difference)
You may download additional directions for measuring the Earth's circumference, and the Data Sheets from the Links page.