Why the sun's rays count as parallel (Aristarchus)
The Greeks already knew the sun was very far away, so rays reaching two cities 500 miles apart are effectively parallel.
The worry
Eratosthenes' method needs the sun's rays at Syene and Alexandria to be parallel. If the sun were close, the rays would spread out like a lamp's and the angle would mean something else. How did he avoid that mistake?
The answer: the sun was already known to be very far away
Around 260 BC, Aristarchus of Samos (air-iss-TAR-kus) estimated that the sun was about 20 times farther than the Moon. He did it with geometry: at half moon, the Sun, Moon and Earth form a right angle at the Moon, and the angle he measured at Earth gave the ratio.
That is far too small; the real figure is about 400 times. But even 20 times was enough to show that two cities 500 miles apart see the sun from almost exactly the same direction. Over that tiny baseline, the rays are parallel for all practical purposes.
Eclipses helped too
During a lunar eclipse, the Earth's curved shadow falls across the Moon. Its size and shape showed the Earth is round and the sun is huge and distant. Aristarchus even concluded that because the sun is so big, it, not the Earth, should be at the center, and the Earth should go around it, some 1,800 years before Copernicus.
Key facts
- Aristarchus (about 260 BC) put the sun about 20 times farther than the Moon; really about 400
- Even that showed the sun's rays are effectively parallel over 500 miles
- Aristarchus proposed a sun-centered system 1,800 years before Copernicus