In the book "Cosmos", Carl Sagan describes the methods used by Eratosthenes in determining the radius of earth (Chapter 1). Going through the steps of the method, he makes the statement "The Sun is so far away that its rays are parallel when they reach the Earth", which is crucial for Eratosthenes' conclusion. Sagan does not explain how Alexandrian scholars knew this quoted fact.

Is it true that the Alexandrian scholars already knew this fact? If yes then how did they determine this or how might they have determined this? Did they know the distance of Sun from Earth? If yes then how?

  • $\begingroup$ Would History of Science and Mathematics be a better home for this question? $\endgroup$ – Qmechanic May 14 '17 at 17:13
  • $\begingroup$ Anybody with basic understanding of geometric optics more or less knows this "fact": rays from a distant point source get closer and closer to parallel as the observer moves away from the source. Parallelism was used as a simplifying assumption in optical treatises at least as far back as Euclid's Catoptrica, see Acerbi's Burning Mirrors $\endgroup$ – Conifold May 14 '17 at 20:44
  • $\begingroup$ Qmechanic - Thanks for pointing out this. I ll ask the related question on that forum. $\endgroup$ – anurag anshu May 17 '17 at 10:36
  • $\begingroup$ @Conifold - I am curious how they knew that sun is "distant". If earth were flat and sun were ask far as Earth's radius, same results would be obtained as were obtained by Eratosthenes. $\endgroup$ – anurag anshu May 17 '17 at 10:37
  • $\begingroup$ It was generally accepted even before the time of Plato that the Earth was round (based on the shadow during lunar eclipses, among other things), and the Sun was much farther than the Moon. Aristarchus estimated it to be 18-20 times farther right before the time of Eratosthenes. $\endgroup$ – Conifold May 17 '17 at 21:06

Eratosthenes knew that the Sun is very far away, although there is a dispute on the accuracy of his estimate of the distance between the Sun and the Earth (https://en.wikipedia.org/wiki/Astronomical_unit#History); the estimate could be spot on or orders of magnitude off, depending on the translation.

  • $\begingroup$ Thanks for the link. I have more questions for the precise method used by Eratosthenes but that more suitably falls under "History of Science and Mathematics". $\endgroup$ – anurag anshu May 17 '17 at 10:34

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