Our piece about the December solstice provoked an interesting discussion. Howard Wilk asked where on the Tropic of Capricorn was the Sun directly overhead at the instant of the solstice. That depends on the time of day – that is, the stage in the Earth’s rotation – at which the instant of the solstice occurs.
I gave a vague answer, and Roberto, in Australia, gave a sharp one: “At the December solstice the sun was directly overhead the point 23 degrees 26 minutes south, 128 degrees 04 minutes east: a very remote spot in the Gibson desert in Western Australia, about 1,000km SE of Broome.”
Yes, so what I should have done was to plot a diagram of that solstice moment, showing the zenithal sunbeam.
Which reminds us of a famous incident in the history of science, involving the other (the northern summer) solstice. As narrated on page 191 of Berenice’s Hair, Eratosthenes (who is said to have been an arrogant man – I picture him as a know-it-all) used the length of a shadow at Alexandria, at noon on the day of the solstice, and the distance straight south from Alexandra to Syene (now Aswan), at the southern end of Egypt, and the report that there, on that one day in the year, the Sun shone vertically down a deep well, to calculate the circumference of planet Earth.
This was around 240 BC; I’m going to say 241, to put it while Berenice was still struggling to govern Egypt before her husband returned from his wars.
Christmas greetings from a rather chilly morning in Canberra.
For your information I got the details of the December solstice from this website https://www.timeanddate.com/worldclock/sunearth.html