HOW SCIENTIST CALCULATED THE EARTH'S CIRCUMFERENCE?

In this modern era, human beings have ability to move from one planet to another planet with the help of rockets. In such an era, it would not be difficult for human beings to find out circumference of the earth. Our highly advance technology is capable to calculate the earth's circumference easily. But if I tell you that 2200 years ago, a mathematician Eratosthenes from ancient Greece found out the whole earth's circumference with the help of just a sticks.

                                                                    

Eratosthenes was a great mathematician and astronomer. The depth of his knowledge and curiosity is observed from one fact that In those day, it took many days for people to travel from one place to another. During those times, Eratosthenes thought of calculating the earth's circumference.

Eratosthenes had heard that in Syene ( An ancient Greece city which was located at south of Alexandria ),  there was no shadow of any vertical object during a summer solstice. It mean the sun was exactly overhead on Syene during summer solstice. When the sun is exactly overhead then there is no shadow that day is called "Zero Shadow Day". Let us discuss little about summer solstice. Summer solstice is astronomical phenomenon occurs when one of the pole of earth tilt maximum toward the sun. Summer solstice typically occurs on June 20 or June 21, bring the longest day and shortest night of the year.

                                                              

By observing summer solstice in Syene, Eratosthenes surprised. At that point  he got a plan and started working on it. Eratosthenes performed an experiment in which he planted a stick into the ground in Syene on June 21 and observed on 12:00 PM ( because at 12:00 PM sun was reached at highest position) that no shadow were caste at noon during summer solstice.                                                                         
 He performed same experiment after one year later at Alexandria then he observed that shadow were caste at noon during summer solstice. He calculated the angle between the stick and dotted line as shown in figure. The angle was measured nearly equal to 7.2°. If we consider the earth is perfect sphere then 7.2° is 1/50 th part of complete circle.

                                                                             
 Now if there is difference between the angle which was measured at Syene and Alexandria, it means that earth must be curved. Eratosthenes already knew about it. Eratosthenes understood that if he could calculated the exact distance between Syene and Alexandria, he would able to find out the whole earth's circumference. But in those day, it was very difficult to calculate exact distance between two cities. Eratosthenes hired Bematists (bematists mean specialists in ancient Greece who were trained to measure distance by counting their steps). then they found that the distance between Syene and Alexandria was 5000 Stadia ( stadia was an ancient Greek unit of length ).

                   

                                 1 Stadia = 176.4 meter

Therefore the distance between Syene and Alexandria = d = 5000 stadia = 5000 * 176.4 = 882000 m

i.e. d = 882 km. By using simple ratio, 

            360° / 7.2° = Circumference of the earth / d

           Circumference of the earth = 50 * 882

                                                          = 44,100 km

But actual earth's circumference is 40,075 km. It means that there was an error in the calculation of Eratosthenes. There was an error of 10.04%. This is how Eratosthenes calculated the Earth circumference 2,200 years ago. Actually, he proved that the Earth is sphere by performing this awesome experiment. 

                                                                

Let us discuss an error. Why there was an error in calculation of Eratosthenes? An error was because of incorrect data. In those day, people didn't know about correct shape of the earth. They considered the earth is in spherical shape. But we know that the earth is flattered at th poles and bulges at the equator. Geodesy ( branch of mathematics which deals with shape and area of the earth) represent the shape of the earth as an oblate spheroid.

                                                

In 2012, Anthony Abreu Mora repeated Eratosthenes method to calculate earth's circumference with the help of correct and accurate data. Then the result was 40,074 km.