It is unlikely that Eratosthenes assumed the Sun was infinitely distant, since he apparently also estimated the distance to the Sun himself. But what Eratosthenes did would make no sense if the Sun were (for example) only $6000$ miles from the Earth. Also an important part of Hellenistic astronomy was access to Assyrian astronomical records going back hundreds of years and presumably done in Mesopotamia. A lunar eclipse allowed him to study the shadow of Earth over the Moon and determined that Earth was twice the size of the Moon rev 2020.10.9.37784, The best answers are voted up and rise to the top, Astronomy Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Solar eclipeses demostrate that the sun is further, but don't say how much further. How did he know it was much farther away than that? Eratosthenes made a calculation by multiplying the distance by the angle. How do we know that the intrinsic brightness of Cepheid variables corresponds to their period? I don't know if one is dependent on the other though. you can tell a light source is far away if an object's shadow is the same size as the object. MathJax reference. In parliamentary republics, why can't the parliamentary election and the presidential election happen on the same day? Is this how Eratosthenes knew it or is this just one way to know it? Is the typo in the 25th amendment significant? Only a second-hand, simplified version. Maybe worth mentioning that Hipparchus measured the distance to the moon by parallax within a century or so of Eratosthenes' work. Knowing the approximate time when a quarter moon is exactly at 50% illumination is very difficult to ascertain. ), but Eratosthenes needed to know that it was immensely farther than that. What should the nonce value be for client-side encryption? What does it mean for particles to "be" the irreducible unitary representations of the Poincare group? The 90degree at first quarter argument says that the distance from earth to sun is many times greater than the distance from earth to moon. How was the Earth-Sun distance originally calculated? Thus the moon must be much further than the radius of the Earth. "And the Sun is further still. The result was 7.12°. To understand the distances involved, he attempted to triangulate the Moon, Sun and Earth. Is it okay to ask a supervisor for the email addresses of their current students? In conclusion, the distance to the sun must be very very large in comparison to the radius of the Earth, and we can assume that that the rays of light from the sun are parallel. The famous measurements and calculations done by Eratosthenes around 300 BC are very widely known. The famous measurements and calculations done by Eratosthenes around 300 BC are very widely known. Astronomy Stack Exchange is a question and answer site for astronomers and astrophysicists. He wouldn't have had the most advanced scientific instruments to measure angles. By observing and measuring shadows on the same day in Alexandra, he calculated that the Sun was over 7.12° from the Zenith on the same date. How do we know galaxy GN-z11 is as far away as it is? The sun and the moon go around the observer once a day, Eratosthenes knew that the apparent size of moon doesn't change. Thus, without modern equipment, he concluded that the speed of light was within measurement error of instantaneous. Is "their" just a misspelling of "they're" in this quote of Melville? Are there celestial bodies that are about as far away as the Sun? He found the angle to be 87° and using the mathematics known at the time he derived the Sun was between 18 to 20 times further away than moon. This is only possible if the sun is much further away than the moon." He was able to determine the Earth's circumference and then another calculation to work out the diameter. Responding to the Lavender Letter and commitments moving forward. @Servaes Fair enough. All good points. Aristarchus concluded that the Sun was much further away than the Moon (by about a factor 20), by claiming that the angle between the Earth, Moon and Sun, when the Moon was half-illuminated, was 87 degrees. Need help finding flaw in the voltage regulator circuit. Asking for help, clarification, or responding to other answers. So everywhere is close to the centre of the moon's orbit. Eratosthenes knew that the Sun was never directly overhead, even on the Summer Solstice, in his home city of Alexandria, which is further north than Syene. Aristarchus was a Greek astronomer who lived at the same time as Eratosthenes and first proposed the idea that the Earth orbited the Sun. Huygens was the first to actually calculate the distance from the Earth to the Sun in 1653. @dandavis : That would probably only tell us that the sun is many miles away (100 miles?? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Co-ordinates: Astronomy > Earth, Moon, Sun > Earth. How to block requests in web app when certificate is insecure? This is only possible if the sun is much further away than the moon. How did Eratosthenes know that the sun is far away? site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Archaeoastronomy. Aristarchus did make a calculation from the Earth to the Sun, but his calculation was off by a factor of 400. sources: Phil Plait's Bad Astronomy: Mad Science Aristarchus of Samos - Wikipedia By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. The distance between the cities was approximately 5000 stadia (back then they measured by stadia – like football pitches are used to quickly illustrate lengths). Later he has heard that each year during the summer solstice, the sun’s rays falling on the bottom of a well in Syene illuminate its entire pit. Aristarchus of Samos and the diameters of the Moon, Sun and their distances. Making statements based on opinion; back them up with references or personal experience. But the apparent size also doesn't change when viewed from anywhere. This is even more remarkable as the town he used as his measurement was not directly to the south and was not exactly on the Tropic of Cancer. At half moon, the sun seems to be at 90∘ to the moon. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. He also knew from the angular size of the Moon and the curvature of the Earth's shadow during a lunar eclipse, that the Moon was a lot further away than the radius of the Earth. Why does \renewcommand error if the command does not exist? What measure of historical accuracy do we retain if we exclude those who report on historical events? Confusingly, there were 2 different measurements for a stadia but scientists believe he used a unit which led to the circumference being within 1 degree of the modern known value. This reminds me of a physics class where a Greek natural philosopher measured the speed of light to be instantaneous, or almost instantaneous. It only takes a minute to sign up. Exactly how Eratosthenes calculated the radius of the Earth has been lost. If the moon were 6000 miles from the Earth, then it would seem to grow and shrink in size as it passed by (such an effect can be seen on Mars, where the moon really does orbit close to the planet). We also now know the angle between a quarter phase moon and the Sun is 89.5° which makes the Sun 400 times further than the Moon but he was accurate in understanding that there was the same ratio between distance and size. What does Trump mean here with "They don’t need more as they are going up for the shot."? It isn't immediately obvious why this should be the case, can you elaborate further? What is the equivalent to Scientific Linux Users as a professional trouble shooting email list for Ubuntu? Select everything besides the Max(date) for each group. And the Sun is further still. It's assuming that the sun is sufficiently far away that the angle between rays from the sun on earth is negligable for this particular computation. At half moon, the sun seems to be at $90^\circ$ to the moon. How does a microcontroller "remember" a program? Today we know Earth is four times larger than the Sun today and Sun and Moon are ½° of arc but it was the best measurement of its time. I think we have this picture of the Greeks in the times of Plato and Aristotle, when they were really mainly in the Aegean (and places like Sicily) and we forget that during the Hellenistic age, Greek culture was much more cosmopolitan! This must mean that Alexandria is near the centre of the moon's orbit. Cleomedes is known for writing down information from third sources ad verbatim, and while I am aware this is a, Also, as far as I'm aware, Eratosthenes didn't believe the sun to be infinitely distant, but rather that the sun's light can be assumed to be, @Flater and many don't.. As for the latter point, that. Wavelengths of colors emitted by alkali metals during flame test. Undecidability of "is this CFG prefix-free?". He then measured the width of both Sun and Moon and determined they were 2° of arc in width. There were several reasons to explain why his measurements were inaccurate. He may also not have access to knowledge about using the mathematical sine function or advanced trigonometry knowledge that may have improved his estimation. He measured the angle between a quarter phase moon (what we call a half moon) and the Sun. Thanks for contributing an answer to Astronomy Stack Exchange! Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. How/when can a doctor say that someone will no longer transmit Covid? A lunar eclipse allowed him to study the shadow of Earth over the Moon and determined that Earth was twice the size of the Moon In any case, his work came after that of Aristarchus who wrote a huge treatise on the distance between the Earth and the Sun and Moon. What is presently taught as his method is a simplified version described by Cleomedes. it was well known that its reflection on this day could be seen directly down a deep well. According to Wikipedia, Eratosthenes was from Cyrene (in modern Libya) and presumably did spend most of his career in Alexandria. The reasoning behind his measurements was good. How did he know it was much farther away than that? He measured the length of the shadow of a tall tower in Alexandria, and used simple … To learn more, see our tips on writing great answers.