The ancient Greek astronomer Eratosthenes measured the Earth\'s circumference wi
ID: 111531 • Letter: T
Question
The ancient Greek astronomer Eratosthenes measured the Earth's circumference with remarkable accuracy. What astronomical observation did he make to accomplish this? He compared the apparent diameter of the Moon at Alexandria with its diameter at Syene. He compared the altitude of the Sun at noon on the summer solstice in Alexandria with its altitude in Syene at the same time. He watched camels disappear below the horizon on their way from Alexandria to Syene. He measured how far north of due west the Sun set on the summer solstice both in Alexandria and Syene.Explanation / Answer
He measured how far north of due west the Sun set on the summer solstice both in Alexandria and Syene.
Eratosthenes lived in the city of Alexandria, near the mouth of the Nile River by the Mediterranean coast, in northern Egypt. He knew that on a certain day each year, the Summer Solstice, in the town of Syene in southern Egypt, there was no shadow at the bottom of a well. He realized that this meant the Sun was directly overhead in Syene at noon on that day each year.
Eratosthenes knew that the Sun was never directly overhead, even on the Summer Solstice, in his home city of Alexandria, which is further north than Syene. He realized that he could determine how far away from directly overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object. He measured the length of the shadow of a tall tower in Alexandria, and used simple geometry to calculate the angle between the shadow and the vertical tower. This angle turned out to be about 7.2 degrees.
Next, Eratosthenes used a bit more geometry to reason that the shadow's angle would be the same as the angle between Alexandria and Syene as measured from the Earth's center. Conveniently, 7.2 degrees is 1/50th of a full circle ( 50 x 7.2° = 360° ). Eratosthenes understood that if he could determine the distance between Alexandria and Syene, he would merely have to multiply that distance by 50 to find the circumference of Earth!
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