Earth's Planetary Size
Speaking from the perspective of the solar system, the Earth is rather small. It has an equatorial diameter of approximately 12,756 km. Even though 4 of the other 8 planets in our solar system are smaller (Pluto, Mercury, Mars, and Venus), the remaining 4 planets (Neptune, Uranus, Saturn, and Jupiter) are much larger.

Around 250 BC, a Greek scientist named Eratosthenes measured the circumference of the Earth with remarkable accuracy. The logic he used is similar to using a single slice of pizza to find the circumference of the entire pie. If you know how large the slice is, and you know how many slices are in the pie, you can calculate the size of the entire pizza. While this logic is easy, in practice it is quite difficult. Using geometry and ingenuity, Eratosthenes found the circumference with amazing accuracy about 1,700 years before Columbus was even born.

Erastosthenes' Method:
1) Determine the distance between his home city of Alexandria and the neighboring city of Syene. This turned out to be about 5,000 stadia (about 780 km).

2) Determine the angular distance on the Earth's surface between the two cities. This is where the geometry comes in. Eratosthenes observed:

• On the Summer Solstice (June 21), the sun was directly overhead in Syene.
• Since the sun was directly overhead, you could see it in the bottom of deep wells, and obelisks did not cast a shadow.
• In Alexandria (his home town) on June 21, obelisks did in fact cast a shadow.

From these assumptions, Eratosthenes concluded that the Earth's surface must be curved. Moreover, he used geometry to reason that the angle of the shadows cast in Alexandria would be equal to the angular distance between the two cities. He measured the shadow angle to be 7 degrees, and concluded that the two cities must be 7 degrees apart on the Earth.

Since the cities were 7 degrees apart, and the Earth is 360 degrees, then the angular distance between the cities must be 1/50 of the circumference of the Earth (7/360).

That meant that the distance between the cities (5,000 stadia) must also be 1/50 of the circumference of the Earth.

He multiplied that distance (5,000 stadia) by 50 to get a total circumference of about 250,000 stadia. This corresponds to about 46,250 km, which is amazingly close to the actual circumference of about 40,000 km!

Web Resources:
Astronomy On-Line: How to measure the size of the Earth
The Librarian who Measured the Earth
Eratosthenes Measures Earth's Circumference
Eratosthenes