Measuring the Earth's radius using a Lego tower and the sun's shadow

More than 2,000 years ago, the Greek mathematician Eratosthenes figured out how to measure the radius of the Earth by comparing the angle of the sun in two different cities. Based on the angle of the shadow and the distance, he calculated the radius of the Earth with an error of less than 1%.

Eratosthenes and the method of measuring the Earth by the sun's shadow. (Source: Bilimintarihi)

Now, physicist Rhett Allain has recreated this experiment in a fun way: using Lego blocks to create a shadow measuring device. With a simple Lego structure, users can measure the length of a shadow, calculate the angle of the Sun, and from there deduce the curvature of the Earth.

The method requires just three things: A friend, a phone for communication, and some Lego blocks. The two people place the Lego devices in two locations hundreds of kilometers apart, measure the shadow at the same time, and compare the angle of deflection. Combined with the distance between the two points, the radius of the Earth can be calculated.

The special thing about Lego is its precision and uniformity in size, which makes experiments easier and more accurate.

Diagram illustrating Eratosthenes' method of using the angle of the sun's shadow and the distance between two cities to calculate the radius of the Earth. (Source: Wired)

How to perform the experiment

According to instructions from WonderHowTo, participants need to prepare about 20 - 30 Lego blocks, a white sheet of paper, a ruler, a camera phone and a friend in another city (at least 100 km away).

Step 1: Build a Lego tower about 13 blocks high (equivalent to 12.48 cm).
Step 2: At noon, take a photo of the tower's shadow and measure the exact length.
Step 3: A friend in another location also takes the measurement at the same time.
Step 4: Compare the shadow angle between the two locations, combine it with the geographical distance (using Google Maps or an odometer), then apply Eratosthenes' original formula or Rhett Allain's modern formula to calculate the Earth's radius.

Physicist Rhett Allain suggests building a Lego tower, measuring the length of the shadow, and then calculating the angle of the Sun using trigonometry.