| Engineering Thermodynamics by J. Pohl © | www.thermomentor.com |
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EratosthenesAround 200 BC, Eratosthenes worked as a librarian in the great library of Alexandria, Egypt. Having seen eclipses of the moon, he believed Earth was spherical. Wells, dug vertically into Earth were common in Egypt. One well at Syrene (now Aswan) was special however.
At noon (on days near the summer solstice) were one to look into the well one would see the full blinding reflection of rays of sunlight. Eratosthenes reasoned that this occurred because the rays of the sun struck Earth perpendicularly. Alexandria was approximately 500 miles due north of the well at Syrene. To measure the angle of incident sunlight there Eratosthenes lowered a plumb bob suspended by a string deep into a well. The sketch shows the angle of the rays at Aswan (zero degrees at noon on the say of summer solstiuce). Also depicted is 7 degree angle measured at Alaxandria at noon on the same day.
Use Eratosthane's data to calculate the circumference of Earth.
♦ The relation between the length of a circular arc, s, radius of the circle, r, and the angle subtended, θ, (in radians) is:
We seek the radius (Earth's radius) associated with a circular arc length of 500 miles with the angle being 7.5 degrees. Placing these numbers in the equation:
But the circumference of a sphere equals its diameter times π :
Today the Earth radius is stated as 3963 miles. Thus, supposing we have the numbers Eratosthene's determined, his measurement of the Earth circumference (some 2000 years ago) was in error only - 0.1%. Very close, indeed!