
#1
Sep712, 01:48 PM

P: 41

1. When the sun was directly overhead in syene, why was it not directly overhead in Alexandria
The size of Earth was first measured in Egypt by Erathosthenes about 235 BC. He calculated the circumference of Earth in the following way. He knew that the Sun is highest in the sky at noon on June 22, the summer solistice. At this time, a vertical stick cast its shortest shadow. If the Sun is directly overhead a vertical stick casts no shadow at all, which occurs at the summer solstice in Syene, a city south of Alexandria (where the Aswan Dam stands today). Eratosthenes learned that the Sun was directly overhead at the summer solstice in Syene from library information, which reported that, at this particular time, sunlight shines directly down a deep well in Syene and is reflected back up again. Eratosthenes reasoned that, if the Sun's rays were extended into Earth at this point, they would pass through the center. Likewise, a verical line extended into Earth at Alexandria (or anywhere else) would also pass through Earth's center. At noon on June 22, Eratosthenes measured the shadow cast by a vertical pillar in Alexandria and found it to be 1/8 the height of the pillar. This corresponds to a 7.1° angle between the Sun's rays and the vertical pillar. Since 7.1° is 7.1/360, or about 1/50 of a circle, Eratosthenes reasoned that the distance between Alexandria and Syene must be 1/50 of the circumference of Earth. Thus the circumference of Earth becomes 50 times the distance between these two cities. This distance, quite flat and frequently traveled, was measured by surveyors to be about 5000 stadia (800 kilometers). So Erastosthenes calculated Earth's circumference be 50 X 5000 stadia = 250,000 stadia. This is very close to the currently accepted value of Earth's circumference. We get the same result by bypassing degrees altogether and comparing the length of shadow cast by pillar to the height of pillar. Geometrical reasoning shows, to a close approximation, that the ratio shadow length/pillar height is the same as the ratio distance between alexandria and syene/Earth's radius. So just as the pillar is 8 times greater than its shadow, the radius of Earth must be 8 times greater than the distance between Alexandria and Syene. Since the circumference of a circle is 2∏ times its radius ( C = 2∏r), Earth's radius is simply its circumference of a divided by 2∏. In modern units, Earth's radius is 6370 kilometers and its circumference is 40,000 km. 2. Relevant equations 3. because the angle 7.1° can correlate to the length of distance between alexandria and syene which is 7.1/360 which would be 1/50 of the earth but a different distance than syene I am sure on another day other than June 22 the sun would be directly over alexandria due to the fact of the Earth's angle and the sun and the earths rotation. 



#2
Sep712, 02:22 PM

P: 2,861

Your answer is incorrect.
The sun can only be directly overhead a town if that town lies between the Tropic of Cancer in the northern hemisphere and the Tropic of Capricorn in the sourthern. Hint: Check the latitude of the tropics as well as Alexandria and Syene. You might wish to change your answer. Hint 2: Read the wikipedia article on Syene 



#3
Sep712, 02:48 PM

P: 41

On Wikipedia I read well what I interpreted from the reading is the Aswan is the driest place on earth 2001 was the first time this place has seen rain in seven years.
The latitude for the Tropic of Cancer is said to be 23° 26′ 16″ The latitude of Alexandria is 31.2000° N, 29.9167° E The latitude of Syene is 24.0667° N, 32.9167° E Oh the Tropic of Cancer and Syene are one of the same O.K. The latitude of the Tropic of Capricorn is 23° 26′ 16″ So would the answer be there are only two spots on planet earth that the Sun can be directly over head and that is in Syene and Chile? 



#4
Sep712, 03:01 PM

P: 2,861

When the sun was directly overhead in syene, why was it not directly overhead in alex 



#5
Sep712, 03:10 PM

P: 2,861

Syene (24°N) is roughly on a tropic (23°N) so at noon on mid summers day the sun will be almost directly overhead. Alexandria (29.9° E) is roughly due north of Syene (32.9° E) so at the same time and date it's easy to compare the length of the shadow. You don't even need to go to Syene you can assume it's zero. 



#6
Sep712, 03:18 PM

HW Helper
Thanks
P: 9,813

Erathosthenes estimated the circumference of Earth but it was more basic that his observations proved that the Earth was not flat. ehild 



#7
Sep712, 03:54 PM

P: 41

With a flat earth there would be no significant angle change? because there would really be no angles other than I guess the suns rotation but if the earth was flat than the sun was something completely different.
Wouldn't the answer be because of the angular differential or something? 



#8
Sep712, 03:59 PM

P: 41





#9
Sep712, 04:22 PM

HW Helper
Thanks
P: 9,813

ehild 



#10
Sep712, 04:28 PM

HW Helper
Thanks
P: 9,813

The Tropic of Capricorn would be appropriate, too. Only the ancient Greeks did not travel there...
ehild 



#11
Sep712, 04:49 PM

P: 41

That's pretty cool one of the first documented discoveries showing the earth had angles actually, a little awesome discovering it as well!! Well for me at least!!



Register to reply 
Related Discussions  
When the Sun is directly overhead, a hawk dives toward the ground with a constant vel  Introductory Physics Homework  5  
Overhead crane and pulleys problem  Classical Physics  6  
Overhead crane and pulleys  Classical Physics  1  
Overhead Cranes Girder  Mechanical Engineering  0  
overhead transmission lines  Electrical Engineering  2 