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
He measured the shadows at noon, the time when the sun is highest in the sky. That can be measured reliably enough with a simple sun dial. A couple of minutes earlier or later won’t make a hige difference in the calculation, frankly the uncertainty of measuring the distance would’ve caused much greater errors
If you travel and measure the angle at the same day in the year, the sun has that same inclination as when you measured the stick at the other location. Within a month the sun’s position doesn’t change much, and the error of your measurements is affected by other things much more
1. Tell your friend to measure the shadow on a stick of a particular length when the sun is at the highest point of the sky on a particular date a few weeks away (or probably a few dates just to be sure in case it’s cloudy on one or two of those days)
2. Travel down to the other place where you want to measure the shadow. There, you do the same thing: using a stick of the same length as your friend’s, measure the shadow when the sun is at the highest point in the sky (again, over a few days to ensure you get some data that can be compared).
3. Come back home and compare notes.
You can figure out what point of the day the sun is highest in the sky by tracking the shadow throughout the day. Whenever the end of the shadow is closest to the stick, that’s when the sun is highest in the sky.
You just have to pick your reference point well
He picked Syene as one of his points because it was known that at solar noon at the summer solstice that there was no shadow at the bottom of the well because the sun shone straight down it.
Solar noon is when the sun is highest in the sky and shadows are shortest, you don’t need a time keep device to find this, just watch your sundial and measure the shadow when its shortest.
Turns out Syene is basically on the tropic of cancer, its about 24 degrees north while the tropic is 23.5 degrees, close enough for his purposes, and the sun was effectively directly overhead of Syene on the summer solstice
So now all he had to do was wait for the summer solstice and measure the length of the shadow of a stick at solar noon(when the shadow is shortest), know the distance to Alexandria (he apparently hired people who specialize in this to find the distance), and do some trig.
Were it not for Syene being located on a tropic he’d have to do additional measurement sets, but you could arrange to do all measurements at solar noon on the summer solstice and everyone could figure out when that is in their location just by watching stick shadows
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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