As you know, Eratosthenes endeavored to measure the circumference of the Earth.
ID: 285180 • Letter: A
Question
As you know, Eratosthenes endeavored to measure the circumference of the Earth. In the process, he determined a certain angle to be about 7.2 degrees. This angle is: (Indicate all that are correct - may be more than one choice correct. However, you will lose credit for picking incorrect choices) The tilt angle of the Earth's axis with respect to the direction perpendicular to the plane of the Earth's orbit around the Sun. The angle between an incoming sunray and the ground in Alexandria on June 21, Summer Solstice day. The angle between a long stick he placed on the ground in Alexandria and the ground there. The angle between incoming sunrays and the zenith direction in Alexandria on june 21, Summer solstice day. The angle between incoming sunrays and the vertically pointing stick that he stood on the ground in Alexandria on une 21, Summer solstice day. QUESTION3 At they landing site on a planet, the sky is cloudy, so that at noon on summer solstice day, the landing party cannot see the Sun in the planet's sky. However, the following facts are known: The circumference of the planet is 70,000 miles. 600 miles directly to the South of the landing site, at noon on summer solstice day the Sun is in the directly overhead direction. From this data, the angle to the Sun in the sky at at the landing site at noon on summer solstice day must be (choose the answer closest to the actual value): 3 degrees O 6 degrees 7 degrees. 5 degrees ( O2 degreesExplanation / Answer
As per norms I should answer for first question only
The angle between incoming sunrays and the vertically pointing stick that he stood on the ground in alexandria on june 21 summer solstice day.
Explanation:
Eratosthenes calculated the circumference of the Earth without leaving Egypt. He knew that at local noon on the summer solstice in Syene(modern Aswan, Egypt), the Sun was directly overhead. (Syene is at latitude 24°05 North, near to the Tropic of Cancer, which was 23°42 North in 100 BC) He knew this because the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. He measured the Sun's angle of elevation at noon on in Alexandria by using a vertical rod, known as a gnomon, and measuring the length of its shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This turned out to be about 7°, or 1/50th the circumference of a circle. Taking the Earth as spherical, and knowing both the distance and direction of Syene, he concluded that the Earth's circumference was fifty times that distance.
His knowledge of the size of Egypt was founded on the work of many generations of surveying trips. Pharaonic bookkeepers gave a distance between Syene and Alexandria of 5,000 stadia (a figure that was checked yearly).[18] Some[who?] say that the distance was corroborated by inquiring about the time that it took to travel from Syene to Alexandria by camel. Carl Sagan said that Eratosthenes paid a man to walk and measure the distance. Some claim Eratosthenes used the Olympic stade of 176.4 m, which would imply a circumference of 44,100 km, an error of 10%,[18] but the 184.8 m Italian stade became (300 years later) the most commonly accepted value for the length of the stade,[18]which implies a circumference of 46,100 km, an error of 15%.[18] It was unlikely, even accounting for his extremely primitive measuring tools, that Eratosthenes could have calculated an accurate measurement for the circumference of the Earth. He made five important assumptions (none of which is perfectly accurate):[18][19]
Eratosthenes later rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia, likely for reasons of calculation simplicity as the larger number is evenly divisible by 60. In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference of the Earth.
Seventeen hundred years after Eratosthenes's death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe, based on a map by Toscanelli, that the Earth's circumference was one-third smaller. Had Columbus set sail knowing that Eratosthenes's larger circumference value was more accurate, he would have known that the place that he made landfall was not Asia, but rather the New World.
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