Measuring The Earth’s Circumference

Long before various astronomical instruments and spacecraft were invented, humans were able to figure out the circumference of the earth. Between 276 BC and 194 BC, Greek mathematician Eratosthenes calculated the circumference of our planet to near accuracy using simple geometric methods.

Over 2,000 years ago, Eratosthenes was already able to estimate the circumference of the earth.

Eratosthenes was an intelligent scholar who worked in Egypt to teach the ruler of Alexandria’s son. During Eratosthenes’ time in Egypt, he heard about a famous well in Syene, Egypt. Every year during the summer solstice, sunlight would be cast directly to the bottom of the well, but it would light up only the water inside of the well and not the walls. Using his knowledge of shadow and light, Eratosthenes suspected that this special phenomenon appeared because the sun happened to be directly above Syene during this time. To prove his theory, Eratosthenes put up a pole in the city of Alexandria during the summer solstice and found that shadows would cast beside the pole, showing that the sun was not directly above Alexandria. With these two pieces of information, Eratosthenes realized that if he could measure the distance between the pole and the well, then measure the angle of the pole’s shadow, it would be possible to calculate the circumference of the earth. He noted that the distance between the two cities was approximately 800km. By using basic trigonometry, he found that the angle of the shadow of the pole was about 7.2 degrees. Hence, Eratosthenes set up the equation “7.2 degrees (arc angle)/360 degrees = 800 km (arc length)/circumference of the earth”. With this equation, he estimated that the circumference of the earth would be about 40,000 km. This is incredibly close to the approximate circumference of the earth that we know today, which is 40,075 km.

Over 2,000 years ago, Eratosthenes was already able to estimate the circumference of the earth with the data he had. It is astonishing to know how the math learned in high school nowadays was applied in the past.

References

“Eratosthenes of Cyrene.” Khan Academy, www.en.khanacademy.org/humanities/big-history-project/solar-system-and-earth/knowing-solar-system-earth/v/. Accessed 28 Nov. 2021.

“Measurement of the Radius of the Earth.” Brain Kart, www.brainkart.com/article/Measurement-of-radius-of-the-Earth_36165/. Accessed 27 Nov. 2021.