As we saw last week, once it became clear to everyone that we live on a spherical Earth, the next question was "how big is it?". Since one can't well go out and measure it directly, indirect methods have to be used -- which brings us back to geometry. And the first person known to have used geometry to estimate the size of our planet was Erathostenes, who at the time was the librarian at the Library of Alexandria.
Erathostenes knew, thanks to travellers, that in the Egyptian city of Syene (currently Aswan) the Sun would be directly overhead at noon on the day of the summer solstice (which means to us that the city sits at the Tropic of Cancer). He also knew that this was not the case for Alexandria, where he lived, and this meant that he could use this difference to calculate the size of the globe.
What he did was to measure the angle of the rays of the Sun in Alexandria at noon on the summer solstice, and using his knowledge of geometry he knew that this was the same angle formed at the centre of the Earth by lines going from there to each of the two cities (Syene and Alexandria). This is a lot of words to explain what can be seen in the (greatly exagerated) figure; the red lines represent the rays of the Sun, each bold dark line represents one of the two cities, and both angles labelled as α are the same. He measured this angle to be 1/50 of a full circle (or 7°12'), and he knew the distance between the two cities to be 5,000 stadia. This, of course, gives us a size of 250,000 stadia for the circumference of the Earth.
And now we have a problem: how much is that, exactly? The answer is, we're not sure; no one knows how much was a stadion for Erathostenes. Archaeological evidence points to a length of 185m to a stadion in Athens, which would result in a circumference of 46,250km, or about 15% larger than reality -- 40,075.16 km. He might have been much closer, though: different places had different stadia, and some evidence points to smaller ones being used in Alexandria. Also, the numbers in his calculations (1/50 and 5,000) are suspiciously round; since we only know of Erathostenes' work through third-party accounts, it is likely that the numbers were rounded at some point and that his calculations were much more precise.
This calculation reinforced the idea that the Earth was fixed, as it was definitely too big to be moved; and, being fixed while everything else moved, it was also clear that it was the centre of the universe.
A few centuries later, in the 1st century AD, another eminent figure tried his hand at calculating the size of the Earth: Ptolemy. He worked using the positions of the stars and their apparent change in position as a person travels, and he reached a circumference of 33,300km. That is very wrong, but since his methods make sense and the results were reproducible, this value was accepted for a long time and was used by everyone until the Middle Ages.
Around the 3rd century AD, the idea of a flat Earth was revived, mostly by Christians who were intent on throwing away all of the "pagan" knowledge of the time. Among the general population, the idea of flat vs. spherical Earth had its ebbs and flows from them on, but among educated people there was never any doubt about the shape of the planet. In the 1300s, with the Renaissance, the spherical Earth stages a come back and this becomes common knowledge once more.
It is at this time that Ptolemy's underestimated numbers had an important effect in history: if we assume that the Earth is only as large as he thought it was, then the western tip of Europe is not that far away from the eastern tip of Asia, and this is one of the factors that inspired the westward navigation of the Portuguese and Spanish in the late 1400s, which resulted in the colonisation of the Americas. As you see, astronomy can indeed change the course of history, and we'll see more examples of this in the future.
That's it for this week. For more detail on this subject, I suggest reading the Wikipedia article on the History of Geodesy. Next week, we'll start to add detail to our map of the Earth and of the sky.
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