Question

How did eratosthenes calculate the circumference of tbe earth?

Answer 1

Hey Dear...

Here is Your Answer =)

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1. Eratosthenes knew that the Sun was directly overhead in the town of Syrene, in northern Egypt, on the Summer Solstice. Since the Sun was directly overhead, a well situated in that town didn’t cast a shadow at its bottom. He also knew that his hometown of Alexandria was further north of Syrene, and the exact distance on foot between the two cities was easily determined.

2. Next, he measured the length of a tall stick called a ‘gnomon’ and stuck it in the ground in Alexandria. When the sun’s rays struck the gnomon, it cast a shadow. Because the sun was directly overhead in Syrene, it had to be obliquely tilted if observed from Alexandria. Hence, a shadow of the stick could be observed in the latter town.

3. The length of the shadow and the actual length of the stick allowed Eratosthenes to calculate the angle of inclination of the Sun. This can be done by taking the inverse tangent of the ratio between the shadow’s length and the stick’s length.

4. The angle labelled “A” is shown in the illustration above. By simple rules of geometry, it can also be observed that A is the angle subtended from the center of the Earth by the distance between the two cities. This angle was found to be nearly 7.2 degrees. (Please refer the image...)

5. Now that Eratosthenes knew the subtended angle and the actual distance between the two cities of Syrene and Alexandria, he could calculate the total circumference of the Earth. The concept he used was very simple.

=>Distance between Alexandria and Syrene = D kilometers

=>Angle subtended by them on the center of the Earth= 7.2 degrees

=>Total angle of a circle= 360 degrees

=>Total Circumference of the Earth= ((360/7.2) x D ) kilometers

# The unit of measurement that was popular in Greece at the time was stadia. Historians have yet to figure out the true length of a single stadia, but popular estimates put it around 160 meters. Eratosthenes estimated the circumference to be 252,000 stades, which is approximately 40,074 kilometers.

# Shockingly enough… the real polar circumference is only 66 kilometers greater than this estimate!

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Hope it Helps You Out =)
Thanks (^^)

Answer 2

Eratosthenes is used to finding out the circumference of the earth by calculating the distance between two cities.

• A Greek mathematician Eratosthenes find out a pole in Alexandria.
• And on the summer season, he found that the pole is casting a shadow.
• So from that he found out the curvature shape of the Earth.
• So with the Earth's curvature and distance between two cities we can find out the planet's circumference.

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