How the circumference of the earth is calculated

To be precise, the Earth is a three-dimensional and the perimeter is a description of a flat figure. It is supposed to calculate the circumference of the Earth's geodetic equator.

To calculate the perimeter, you have to know the radius.

The shape of the Earth approximates a sphere, so how to measure its radius? It is said that the radius of the Earth was first measured by the Greek astronomer Eradocenes in the third century BC.

He found that on the day of the summer solstice, when the sun shone directly on the well S in the city of Sai (now the city of Aswan, Egypt), the zenith of a point A in Alexandria and the sun's angle of 7.2 ° (the zenith is a plumbline upward infinitely extended and the sky, "the celestial sphere" intersected the point). He believed that these two places were on the same meridian, and thus the arc between these two places is the angle of the circle SOA is 7.2 ° (Figure 1). Knowing that the distance between A and S was measured to be about 5,000 arshins when the caravan was traveling, he calculated the radius of the earth to be about 4,000 arshins according to the relationship between the length of the arc and the angle of the center of the circle. It is generally accepted that 1 Grecian mile is about 158.5 meters, so he measured the radius of the Earth to be about 6340 kilometers.

The radius is known, so the circumference of the equator is 2πR