Eratosthenes Shadow

Eratosthenes was a Greek mathematician, poet, and astronomer, but he is most famously known for being the first person to make a measurement for the size of the Earth. Over 2000 years ago, at the city of Syene, the sun’s rays fell upon a temple column casting a shadow, (1). The scientist noticed that as the sun reached midday, the shadow would not be casted since the sun was directly over the column. However, 800 kilometers to the north in the city of Alexandria, at the same moment at noon, there was a shadow displayed from a different column, (1). This made him wonder as to how a shadow could be seen from an object in one city and not seen in another at the same time. Being the scientist that he was, he theorized that in order for this …show more content…
For fulfilling this first task, he hired someone to measure the distance between the two cities by pacing the entire way, which came to be 800 kilometers, (1). Due to the sun’s rays falling vertically down on the Earth, Eratosthenes was able to measure the angle cast from the temple in Alexandria, since the sun was directly overhead in Syene. He either took a sundial, a protractor, or some other contraption to give him the degree measurement of the shadow from the top of the tall tower, which came to be around 7.2 degrees, (3). Plus, he also knew that the Earth was round in shape, so a full circle would be 360 degrees, meaning that 7.2 degrees would be one-fiftieth of the circumference, since 360 divided by 7.2 = 50. So with this information he set up an equation that had the total degrees of the circumference of the earth multiplying the distance from Alexandria to Syene, and then dividing that by the degrees of the shadow which solved the circumference of the Earth. 360 degrees*800 kilometers/7.2 degrees = 40,000 kilometers, (3). From solving his equation, he found that 40,000 kilometers was the measurement of the circumference of the Earth, or 250,000 stadia-which was the measurement he had used, …show more content…
People would have to first mark what pillars, or other objects, they want to use in the two cities and measure the distance. Most likely they’ll use Google Earth to answer that instead of personally measuring out the entire trip, because no one would want to do that. Then by taking a visit to Nasa’s webpage, they can look up their scientific measurement of the circumference of the Earth, which is said to be 40,030.2 km, (4). Next, people would take the formula that Eratosthenes developed to calculate the circumference of the Earth, but instead they would discover what the central angle is. 360 degrees*800 km/40,030.2 km = the central angle, which gives 7.19 as the degree measure. The order in which the measurements were discovered may be different than Eratosthenes, but it will still give people the same angle that he had discovered over 2000 years ago. It is mind boggling that with little to no outside resources he was able to come up with the calculation of the Earth’s circumference as 40,000 km, compared to a more accurate measure of 40,030.2 km, (4). By knowing that his data for the circumference of the Earth was around 40,000 km, we just divide that number by 2 to give us 20,000 km, for his estimated radius of the Earth. This estimated radius of 20,000 km is not that far off from