[00:01] learned about you know the technique for measuring the radius of the Earth I think I saw so there's this old TV series called Cosmos and uh the way the story goes is that he had read somewhere of this well in this town called sinin
[00:14] in Egypt uh where on one day of the year the summer soltice you could look down in the well and you could see the sun reflected in the water underneath and he said oh that's kind of cool uh um I don't live there but I have a well in my
[00:27] the same thing so he wait until the summer solstice and he at noon he went down and looked at the well and there was no reflection of the Sun and he knew round let's think of the Sun as far enough away from Earth that all of its
[00:42] rays of light are effectively parallel at any given moment if you draw a line from the center of the earth straight to the sun it passes through some point on the surface which must be experiencing this phenomenon where the sun is
[00:54] directly overhead but if you were someone in aatosan time it would be very difficult to know exactly where this was happening at a given moment so what makes the summer solstice special is that on that day the axis of Earth's
[01:08] rotation is tilted directly towards the Sun and as a result on this day as the Earth revolves around that axis over 24 hours there's a consistent line of latitude where all of the locations on this line predictably experience this
[01:24] phenomenon this line has a special name it's called the Tropic of Cancer and the town cine that aatosan had read about sits on this line now aatosan himself was in Alexandria which is a bit north of that so the direction that he
[01:37] perceives as straight up is going to sit at a certain angle away from the Rays of that Sun so by measuring that this angle was about 7° he could reason that the arc along the planet Earth between his Town Alexandria and Cen is about 7° so
[01:53] if you take the ratio between this angle and the full 360° around a circle that should be the ratio of the distance between his town and Cen and the full know that distance you can deduce the size of the Earth