How Did Eratosthenes Measure the Size of the Earth

Measuring the size of the Earth is no easy task, but over two thousand years ago, a Greek mathematician and astronomer named Eratosthenes cracked the code and calculated the Earth’s circumference with astonishing accuracy. His method was not only innovative but also the foundation for many future scientific advancements. So, how did Eratosthenes measure the size of the Earth?

Eratosthenes’ journey to measuring the Earth’s circumference started with a simple observation. He noticed that during the summer solstice, the sun was directly overhead in the Egyptian town of Syene (now Aswan), casting perfectly vertical shadows. Intrigued by this phenomenon, he wondered if the same could be observed in his hometown, Alexandria.

To test his hypothesis, Eratosthenes decided to conduct an experiment during the summer solstice. He placed a vertical stick in Alexandria and measured the angle of the shadow it cast at noon. Surprisingly, the shadow was not vertical but formed an angle with the stick. Eratosthenes reasoned that this difference in shadow angles was due to the curvature of the Earth.

With this information, Eratosthenes set out to measure the Earth’s size. He knew that the distance between Alexandria and Syene was approximately 800 kilometers, and he assumed that the Earth was a sphere with a perfectly curved surface. Recognizing that a circle contains 360 degrees, Eratosthenes reasoned that the angle formed between the vertical stick and its shadow was proportional to the arc length between Alexandria and Syene.

Using his angle measurement, Eratosthenes calculated that the angle formed equaled about 1/50th of a circle. Therefore, he concluded that the distance between Alexandria and Syene was 1/50th of the Earth’s circumference.

To determine the Earth’s full circumference, Eratosthenes multiplied the distance between Alexandria and Syene (800 kilometers) by 50. His final estimation of the Earth’s circumference was around 40,000 kilometers, which was remarkably close to the actual value of 40,075 kilometers.

Eratosthenes’ calculation of the Earth’s circumference was groundbreaking. Not only did it demonstrate the Earth’s spherical shape, but it also provided a method for measuring its size. This discovery opened the doors to further exploration and scientific advancements in geography and astronomy.

Moreover, Eratosthenes’ method of measuring the Earth’s size had a lasting impact on future generations. It inspired countless scientists to refine his calculations and develop more accurate methods. His work laid the foundation for important developments such as the creation of maps and globes.

In modern times, we have advanced technologies like satellites and GPS that give us precise measurements of the Earth’s circumference. However, Eratosthenes’ innovative approach using simple observations and mathematical deductions remains a testament to the power of human curiosity and ingenuity.

In conclusion, Eratosthenes, the Greek mathematician and astronomer, revolutionized the understanding of the Earth’s size by measuring its circumference with remarkable accuracy. Using the angle of shadows during the summer solstice, he devised a method that allowed him to estimate the Earth’s circumference, which closely matched the actual value. Eratosthenes’ ingenious approach opened new horizons in geography and astronomy, leaving a lasting impact on scientific exploration for centuries to come.