About the Image
How Do We Calculate Distances of This Magnitude?
How do we convert to kilometers? Well, we believe that the unit of the "stadium" was about 0.15 km. This means that Eratosthenes estimated the circumference of the Earth to be about 40,000 km. He also knew that the circumference of a circle was equal to 2 times p (3.1415...) times the radius of the circle. (C=2 p r) With this information, Eratosthenes inferred that the Earth's radius was 6366 km. Both of these values are very close to the accepted modern values for the Earth's circumference and radius, 40,070 km and 6378 km respectively, which have since been measured by orbiting spacecraft.
The diameter of a circle is twice the radius, giving us a diameter for Earth of 12,756 km.
Note: The Earth is almost, but not quite, a perfect sphere. Its equatorial radius is 6378 km, but its polar radius is 6357 km - in other words, the Earth is slightly flattened. Eratosthenes was measuring the polar radius, and his value (using the 0.15 km/stadium conversion) lies between the polar and equatorial values.
Image Credit for Earth image in this section: Clementine, Naval Research Laboratory. It is copyright free.
Why Are These Distances Important To Astronomers?
During the 18th and 19th centuries, astronomers used the diameter of the Earth as the basic yardstick in determining the size of the solar system. Today's astronomers usually do not need to know the size of the Earth for their daily research activities. Nevertheless, the diameter of the Earth still is the first step for us, the residents of this planet, in our attempt to understand the cosmic distance scale.
The Space Shuttle orbiter, with a velocity of 27,880 km per hour (17,322 miles per hour) takes approximately 90 minutes to orbit, or travel just outside the circumference of the Earth. At an altitude of 322 km (200 miles), an orbiter covers approximately 41,300 km (26,000 miles) in one orbit.