

Our calculationsAccording to the EARTH SYSTEM RESEARCH LAB (screen shot right), OREC has a latitude (northsouth distance) of D.d 45.74. We have chosen to collaborate with Shirebrook School in England, whose latitude is D.d 53.2  different enough to give a significant difference in measurements.
We chose a date, March 29th, near to the Spring Equinox, and placed a standard meter stick vertically on the ground at solar noon local time (see right). Students placed a piece of white paper on the ground so they could observe and measure the shadow created by the stick. They marked on the paper the end of the shadow at one minute intervals over a ten period around solar noon. Students then determined the length of the shortest shadow, which should be local high solar noon (see EARTH LAB for time) Back in the classroom, students made a diagram of the triangle created by the stick, its shadow and the hypotenuse (end of shadow to top of stick). Using Tan = opposite/adjacent, students could find the ‘sun angle’ – that is, the angle between the hypotenuse and the top of the stick. OREC found the sun angle to be 44.5 degrees Shirebrook School found the sun angle to be 50.9 degrees The difference between these two angles is the same as the angle formed by the intersection of a line drawn from the stick in Oxford through the centre of the Earth, and a line drawn from Shirebrook School through the centre of the Earth. This is called the central angle, which is 6.4degrees We have created a ‘slice’ of the Earth. How many of these ‘slices’ make up the full circle of the Earth? We need to divide 360 degrees (the circle of the Earth) by our central angle, which is 6.4 = 56.24 slices or sectors. Erathosthenes had someone measure the northsouth distance between the two places whose sun angles he calculated. We have taken a shortcut and worked out the distance fro, the known latitudes of each school, and the fact that each 1 degree of latitude is approximately 111km. So, the distance of the edge of our slice is the difference in latitude between the two schools multiplied by 111 – that is 7.46 x 111 = 828.06km Now we multiply the number of slices by the distance of the edge: 56.24 x 828.06 km = 46 578 km This is our calculation of the circumference of the Earth. The actual circumference of the Earth (through the poles) is 40 008km. The difference between our result and the actual circumference is 6570 km, a percentage error of 8.5%. Erathosthenes had a percentage error of 3%. We will continue to improve our experimental method and measurements. Many thanks to the students and teachers of Shirebrook Academy. Thanks too, of course, to Erathosthenes! For further details of this experiment, contact aldredm@ccrsb.ca or Miss Bath at Shirebrook Academy 
Oxford Regional Education CentreShirebrook Academy 