NOTE: I’m not a flat-earther, but have curiosity.
Seeing that famous clip of Carl Sagan explaining the Erathostenes experiment with the shadows of the pillars in Sion and Alexandria a question comes to me, how he knows the position of the shadow in the other site at the same hour? I mean, there were reliable clocks or time measuring methods at that time in order to be sure once traveled from one place to another that he was at the same hour of the day measuring the shadows?
Thanks in advance!!
In: 2
For all practical purposes [Syene](https://en.wikipedia.org/wiki/Aswan) is due south of [Alexandria](https://en.wikipedia.org/wiki/Alexandria.) (You can check the coordinates.)
So they share the same [apparent solar time](https://en.wikipedia.org/wiki/Solar_time), meaning that when it is noon in Syene it is also (up to some negligible minutes) noon in Alexandria. **No clock needed.**
On that special day in the year the sun is exactly overhead (at the zenith) in Syene: sun, Syene and earth center are aligned.
At the same time the sun is *not* at the zenith in Alexandria, but at an angle to the vertical, an angle which can be measured from the shadow of a vertical stick, pillar, &c.
Geometry (see [picture](https://i.imgur.com/568T4jw.png) roughly slapped together) then shows that that angle in Alexandria is equal to the angle between Alexandria and Syene *as seen from the center of the earth*, supposing the sun is infinitely far away so that its rays are parallel.
Knowing that angle and the distance along earth’s surface (“road distance”) from Alexandria to Syene one can compute the radius of the circle, i. e. earth’s radius.
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