Question

Explain in detail the Eratosthenes method of finding the radius of Earth.

Answer 1

                                 Measuring the radius of the Earth

Eratosthenes observed that during noon time of summer solstice the Sun’s rays cast no shadow in the city Syne. It was located 500 miles away from Alexandria. On the same day and the same time, he found that in Alexandria the Sun’s rays made an angle of 7.2 degrees with local verticals as shown in the figure. He realized that this difference of 7.2 degrees was due to the curvature of the Earth.

The angle of 7.2 degrees is equivalent to `1/8` radians. So θ = `1/8` rad.

If S is the length of the arc between the cities of Syne and Alexandria, and if R is the radius of Earth, then,

S = Rθ = 500 miles

So, the radius of the Earth.

R = `500/θ` miles

R = 500 `"miles"/(1/8)`

R = 4000 miles

1 mile is equal to 1.609 km. So, he measured the radius of the Earth to be equal to R = 6436 km, which is amazingly close to the correct value of 6378 km.