1. Size of the Earth How a scientific proof works.

2. How big is Earth? Having established its shape, what is Earth’s size? Having established its shape, what is Earth’s size? How do you measure something really big? How do you measure something really big? Eratosthenes devised a way to determine the size of Earth around 200BC. Eratosthenes devised a way to determine the size of Earth around 200BC.

3. Eratosthenes Based his calculation on observations of the sun on June 20 in Alexandria and Syene – two cities 5000 stadia apart (500 miles) in Egypt. Based his calculation on observations of the sun on June 20 in Alexandria and Syene – two cities 5000 stadia apart (500 miles) in Egypt. On this date, the sun was straight overhead at noon in Syene, but 7.5 o south of overhead at Alexandria On this date, the sun was straight overhead at noon in Syene, but 7.5 o south of overhead at Alexandria

4. Syene Alexandria Syene Alexandria

5. Eratosthenes Made assumptions that… Made assumptions that… –the Earth is spherical, and –the sun’s rays are parallel Using simple geometry, he set up an equation to determined the circumference of Earth. Using simple geometry, he set up an equation to determined the circumference of Earth.

7. Eratosthenes’ Result Earth’s circumference is 240,000 stadia (about 39,250 km or 23,900 miles) Earth’s circumference is 240,000 stadia (about 39,250 km or 23,900 miles) This is quite close to modern equatorial measurements (24,900 miles). This is quite close to modern equatorial measurements (24,900 miles). From his knowledge of geometry, he was able to calculate the radius of Earth, r. From his knowledge of geometry, he was able to calculate the radius of Earth, r. Circumference = 2  r Circumference = 2  r