PROBLEMS-THE EARTH Task 1: circumference and radius of the Earth The Greek mathematician Eratosthenes, in around 250 BC, is famous for measuring the circumference of the Earth. He knew that at the summer solstice the sun shone directly into a well at Syene...
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PROBLEMS-THE EARTH Task 1: circumference and radius of the Earth The Greek mathematician Eratosthenes, in around 250 BC, is famous for measuring the circumference of the Earth. He knew that at the summer solstice the sun shone directly into a well at Syene (now Aswan) at noon. He found that at the same time, in Alexandria, Egypt, approximately 5000 stadia (1 stadium ≈ 0.1 mile≈0.16 km) due north of Syene, the angle of inclination of the sun’s rays was about 7.2°. With these measurements he computed the diameter and circumference of the earth as shown below. 1. Show that = ’. 2. Complete the following table of proportionality. Angle ’ 7.2° Length (stadia) 5000 Length (km) 3. Deduce the diameter of the Earth considering it’s a sphere. 4. Find the current measured circumference and diameter of the Earth and compare with Eratosthenes’ result: compute the relative error he made and comment. Task 2 Mean radius The Earth is flattened at its poles. This flattening is 1 298 , i.e. the polar
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