How Large is the Earth? And How Do We Measure It?How large is the Earth, and how do we know that? Greek mathematician Eratosthenes calculated the size of the Earth in 200BC with a stick!
How Large is the Earth? This is how Eratosthenes calculated the size of the Earth in 200 BC using just a stick. Eratosthenes wasn't able to directly measure the Earth, but he did realise that it could be measured in a roundabout and inventive way.
One day in Syene (modern-day Aswan in Egypt), Eratosthenes knew that the Sun would be directly overhead as it was the Summer Solstice. He travelled 5,000 stadia to Alexandria, a stadia being an ancient Greek unit of length based on the length of a typical sports stadium. Five thousand stadia are approximately 8,900 kilometres. There, he set a stick in the ground. At midday, when the Sun was at its highest, he measured the angle of the shadow that the Sun formed on the ground, which he measured to be 7.2°.
In this diagram, pretend Syene is at the top of the Earth in this diagram, and Alexandria is in the UK. Eratosthenes knew the angle between the Sun and Alexandria, and since both angles are the same, he could extend this to the Earth's centre. Then, from the parallel rays of light from the Sun. Since Eratosthenes knew the angle between the Sun and Alexandria, and both angles were the same, he could extend this to the Earth's centre.
Since the two angles are the same, they must represent the distance between the two cities. Since there are 360° in a circle, he calculated that 5,000 stadia is approximately one-fifth of the circumference of the Earth.
Using this, he went on to suggest that the circumference of the Earth is 250,000 stadia or 40,000 - 46,000km. He then went further and, using the works of Pythagoras, he could calculate the Earth's radius.
Equation 1 - Circle, circumference of
Equation 6 - Radius of a Circle
Equation 7 - Radius of the Earth solved
The value of the Radius of the Earth that Eratosthenes calculated was around 6,366km to 7,321km. The value is around this because there are no accurate measurements of how long a stadium is. Eratosthenes assumed that Syene and Alexandria were on the same line of longitude. However, they are not.
Astronomers have since measured the Earth accurately using satellite-based laser measuring equipment and recorded a figure of 40,008 km for the circumference of the Earth and the Earth's radius, 6,367km! Considering the difference in equipment between Eratosthenes and modern-day scientists, Eratosthenes did a fine job!
Eratosthenes' curiosity went far beyond the Earth. He also considered some of the astronomical questions of his day, including the distance to the Sun and the Moon.
