Astronomy

How Was the Earth’s Radius First Measured?

umasundresh 27 Jun 2025 No Comments

The Genius of Eratosthenes (Around 240 BCE)

Eratosthenes, a Greek mathematician, was the first known person to measure the Earth’s radius — over 2,200 years ago, without any satellite or GPS!

Here’s how he did it using just shadows and math:

The Shadow Trick

Eratosthenes lived in Alexandria, Egypt. He heard that in another Egyptian city called Syene (modern-day Aswan), something curious happened every year on June 21, the summer solstice:

At noon, the Sun was directly overhead. Deep wells and tall pillars cast no shadows!

But in Alexandria, at the same time, shadows appeared. This gave Eratosthenes an idea.

So, Eratosthenes:

Put a stick straight up in Alexandria, and he measured the angle of the shadow. Found it was about 7.2 degrees, like a slice of pizza from a big circle!

He thought: “If the Earth were flat, the Sun would shine the same everywhere. But if the Earth is round, the sunlight hits different places at different angles. Aha!”

Integrating Everything Effectively

what Eratosthenes did was:

Measured the angle of the Sun’s rays off vertical in Alexandria: 7.2°

Inferred that this angle equals the central angle between Alexandria and Syene.

Since a full circle has 360°, and 7.2° is a slice of that:

\begin{equation}
\frac{7.2}{360}=\frac{1}{50}
\end{equation}

The arc between the two cities is 1/50th of Earth’s total circumference, He already knew the distance between the cities: approximately 800 km.

Therefore, Earth’s circumference=800×50=40,000 km

That estimate is amazingly close to the modern measurement of the Earth’s average radius: 6,371 km!

Then using the formula for circumference of a circle:

C=2πr

We can solve for radius: r= C2π = 40,000(2π) ≈ 6,366 km

Other Cool Things He Did

• Invented the word “geography” , which means “writing about the Earth.”
• Drew some of the first world maps with lines of latitude and longitude.
• Created a method to find prime numbers, called the Sieve of Eratosthenes , still taught in math today!

Try This at Home!

Put a stick in the ground and watch the shadow during the day. How does it change? You’re doing shadow science, just like Eratosthenes!