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

by pbody
Tags: alex, directly, overhead, syene
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pbody
#1
Sep7-12, 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.
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CWatters
#2
Sep7-12, 02:22 PM
P: 3,243
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
pbody
#3
Sep7-12, 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?

CWatters
#4
Sep7-12, 03:01 PM
P: 3,243
When the sun was directly overhead in syene, why was it not directly overhead in alex

Quote Quote by pbody View Post
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.
I meant this bit...

The latitude of the city that would become Aswan located at 24 5′ 23″ was an object of great interest to the ancient geographers. They believed that it was seated immediately under the tropic, and that on the day of the summer solstice, a vertical staff cast no shadow. They noted that the sun's disc was reflected in a well at noon. This statement is only approximately correct; at the summer solstice, the shadow was only 1/400th of the staff, and so could scarcely be discerned, and the northern limb of the Sun's disc would be nearly vertical.
Alex is too far north for the sun to ever be directly overhead. The earth doesn't tilt that much.
CWatters
#5
Sep7-12, 03:10 PM
P: 3,243
Quote Quote by pbody View Post
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?
No it can be overhead anywhere between the tropics (at different times of the year).

Syene (24N) is roughly on a tropic (23N) 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.
ehild
#6
Sep7-12, 03:18 PM
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Quote Quote by pbody View Post
1. When the sun was directly overhead in syene, why was it not directly overhead in Alexandria

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.
Siene is at the Tropic of Cancer, and Alexandria was due north of Syene. So the sun is never overhead in Alexandria. The question is why the sun is not overhead in both town at noon, on the same day. Hint: what would be the situation with a flat Earth?
Erathosthenes estimated the circumference of Earth but it was more basic that his observations proved that the Earth was not flat.

ehild
pbody
#7
Sep7-12, 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?
pbody
#8
Sep7-12, 03:59 PM
P: 41
Quote Quote by CWatters View Post
I meant this bit...



Alex is too far north for the sun to ever be directly overhead. The earth doesn't tilt that much.
Can the same experiement be done at the Tropics of capricorn with the same calculations of a fraction of a shadow or only in the Tropics of Cancer?
ehild
#9
Sep7-12, 04:22 PM
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Quote Quote by pbody View Post
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?
If the Earth was flat the Sun rays would make the same angle with the surface at the same time. Erathosthenes knew that the Sun shined into that deep well in Syene at noon June 22, but it cast shadow in Alexandria at the same time. So the surface of the Earth must be tilted with respect to the sun rays in Alexandria, while it is normal to the rays in Syene : it must be curved.

ehild
ehild
#10
Sep7-12, 04:28 PM
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The Tropic of Capricorn would be appropriate, too. Only the ancient Greeks did not travel there...

ehild
pbody
#11
Sep7-12, 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!!


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