What is A Shadow Stick?
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 a location
on the same longitude but at a different latitude. For SunShIP all locations will
use the equator (0 degrees latitude) and their own local latitude for the 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 two locations in kilometers needs 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 between two locations * (360/angle difference)
You may download additional directions for measuring the Earth's circumference,
and the Data Sheets from the Links page.