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Eratosthenes and the curvature of the Earth Options
lazarius
Posted: Saturday, June 15, 2019 9:06:45 AM

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I'm reading Carl Sagan's "Cosmos" and he thus recounts the story of Eratosthenes' calculation of the Earth's circumference:



Now I wonder how this queer thought could possibly cross his mind. Isn't it quite obvious that the Sun is suspended at a height of 6371.3 km plumb above Syene and casts oblique rays at Alexandria?

-

Come share with me the oceans - oceans of fantasy.
Gary98
Posted: Saturday, June 15, 2019 10:31:13 AM

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The sun is so far away its rays to different points of earth are almost parallel. Consider they are parallel. If the earth is flat, sticks placed at different places on earth should have the same length of shadow (their angles to the rays of the sun are the same). If the surface of the earth is curved, sticks at different places will have different angles to the rays of the sun hence they have different lengths of shadows.

Since stick's shadows at different places have different lengths, the surface of the ear must be curved.

Why don't I come up with something like this?
Clyde of Oz
Posted: Monday, June 17, 2019 6:59:00 AM

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I think the point lazarius is making is: how did they know the sun was far enough away that its rays were essentially parallel?

“Somewhere, something incredible is waiting to be known.” ― Carl Sagan
Blodybeef
Posted: Wednesday, July 3, 2019 1:53:11 AM

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Quote:
I think the point lazarius is making is: how did they know the sun was far enough away that its rays were essentially parallel?


Because in their time the only way to harvest Helium was to catapult people with big silk cargo bags to upper layers of atmosphere.



There they would open their bags to collect as much helium as they could, and return to earth, easing their falls with the help of helium they have collected.

Every once in a while when they collected more helium tan their body weight could not counter, they would return to their farms, by the help of silken threads tied to their ankles, which are secured to anchors on their farms. These threads would traditionally be around 6500 meters.

I believe the remaining math would be guess work; "I'm 6500 meters in the sky and the sun is still too far away, so let's factor in x1000, aaand here, we have an approximate distance of the sun."

Whistle

“Integrity is doing the right thing, even when no one is watching." ― C.S. Lewis
Drag0nspeaker
Posted: Wednesday, July 3, 2019 6:46:41 AM

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Clyde of Oz wrote:
I think the point lazarius is making is: how did they know the sun was far enough away that its rays were essentially parallel?

Ah - that's because their visitors from the Pup (Sirius B, companion of the Dog Star) TOLD them.
It's always good to have knowledgeable friends.


Wyrd bið ful aræd - bull!
Kampong
Posted: Saturday, July 6, 2019 1:27:55 AM
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Sun-rays could be assumed to be parallel, as they were definitely above the clouds: The clouds passes in front
the sun is definitely above the moon: the sun is occasionally eclipsed by the moon.
the moon is much closer to the earth than the sun as the shadow of the moon only covers a limited surface , yet its apparent size is about the same as the sun-disk.

Thus - while having no clue about the true size of the solar system ( that was only achieved by measuring the time the transit of Venus takes across the sun-disk (1769)) it was a hypothesis that could be substantiated.
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