Size of the EarthSize of the Earth

How a scientific proof works.How a scientific proof works.

How big is Earth?How big is Earth? Having established its shape, what is Having established its shape, what is

Earth’s size?Earth’s size?

How do you measure something How do you measure something really big? really big?

Eratosthenes devised a way to Eratosthenes devised a way to determine the size of Earth around determine the size of Earth around 200BC. 200BC.

EratosthenesEratosthenes

Based his calculation on observations Based his calculation on observations of the sun on June 20 in Alexandria of the sun on June 20 in Alexandria and Syene – two cities 5000 stadia and Syene – two cities 5000 stadia apart (500 miles) in Egypt. apart (500 miles) in Egypt.

On this date, the sun was straight On this date, the sun was straight overhead at noon in Syene, but 7.5overhead at noon in Syene, but 7.5oo south of overhead at Alexandriasouth of overhead at Alexandria

Syene AlexandriaSyene Alexandria

EratosthenesEratosthenes

Made assumptions that…Made assumptions that…– the Earth is spherical, andthe Earth is spherical, and– the sun’s rays are parallelthe sun’s rays are parallel

Using simple geometry, he set up an Using simple geometry, he set up an equation to determined the equation to determined the circumference of Earth.circumference of Earth.

Eratosthenes’ ResultEratosthenes’ Result

Earth’s circumference is 240,000 stadia Earth’s circumference is 240,000 stadia (about 39,250 km or 23,900 miles) (about 39,250 km or 23,900 miles)

This is quite close to modern equatorial This is quite close to modern equatorial measurements (24,900 miles).measurements (24,900 miles).

From his knowledge of geometry, he From his knowledge of geometry, he was able to calculate the radius of Earth, was able to calculate the radius of Earth, r.r.

Circumference = 2Circumference = 2rr