What is presently taught as his method is a simplified version described by Cleomedes. 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. This is approximately 1/50th of a circle. To learn more, see our tips on writing great answers. In the same sense as assuming a massless string doesn't mean you think the string has zero mass. Only a second-hand, simplified version. Geocentric & Heliocentric Models Is it okay to ask a supervisor for the email addresses of their current students? Thus the moon must be much further than the radius of the Earth. He was able to determine the Earth's circumference and then another calculation to work out the diameter. 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. The famous measurements and calculations done by Eratosthenes around 300 BC are very widely known. it was well known that its reflection on this day could be seen directly down a deep well. He realized that he could determine how far away from directly overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object. What does it mean for particles to "be" the irreducible unitary representations of the Poincare group? There were several reasons to explain why his measurements were inaccurate. But what Eratosthenes did would make no sense if the Sun were (for example) only $6000$ miles from the Earth. But we don't know what was assumed because there is no account of it. This is only possible if the sun is much further away than the moon. In parliamentary republics, why can't the parliamentary election and the presidential election happen on the same day? This reminds me of a physics class where a Greek natural philosopher measured the speed of light to be instantaneous, or almost instantaneous. Responding to the Lavender Letter and commitments moving forward. The distance between the cities was approximately 5000 stadia (back then they measured by stadia – like football pitches are used to quickly illustrate lengths). He learnt that near the town of Syene (named Aswan today), to the south, the Sun appears at the zenith (the highest point in the sky) on the summer solstice. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. How did Ptolemy prove in the following excerpt that the Earth is not cylindrical? The reasoning behind his measurements was good. But what Eratosthenes did would make no sense if the Sun were (for example) only $6000$ miles from the Earth. @dandavis : That would probably only tell us that the sun is many miles away (100 miles?? The result was 7.12°. He wouldn't have had the most advanced scientific instruments to measure angles. The sun and the moon go around the observer once a day, Eratosthenes knew that the apparent size of moon doesn't change. Do laws on 'drones' in Australia apply to fixed wing model aircraft? All good points. He may also not have access to knowledge about using the mathematical sine function or advanced trigonometry knowledge that may have improved his estimation. Making statements based on opinion; back them up with references or personal experience. He then measured the width of both Sun and Moon and determined they were 2° of arc in width. Also an important part of Hellenistic astronomy was access to Assyrian astronomical records going back hundreds of years and presumably done in Mesopotamia. You may be thinking of Aristarchus of Samos (born 310 BC). Use MathJax to format equations. But the apparent size also doesn't change when viewed from anywhere. Ancient Observations He concluded correctly that the circumference of the Earth is about $252\,000$ times the length of an athletic stadium. 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. 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. Knowing the approximate time when a quarter moon is exactly at 50% illumination is very difficult to ascertain. How does a microcontroller "remember" a program? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. How was the Earth-Sun distance originally calculated? Need help finding flaw in the voltage regulator circuit. 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. 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. And the Sun is further still. 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. 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. Archaeoastronomy. How do we know galaxy GN-z11 is as far away as it is? Can a precognitive dodge modern firearms? According to Wikipedia, Eratosthenes was from Cyrene (in modern Libya) and presumably did spend most of his career in Alexandria. @Servaes Fair enough. This is only possible if the sun is much further away than the moon." What should the nonce value be for client-side encryption? 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 How did he know it was much farther away than that? 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. It only takes a minute to sign up. It isn't immediately obvious why this should be the case, can you elaborate further? 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. Select everything besides the Max(date) for each group. 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 Is "their" just a misspelling of "they're" in this quote of Melville? Aristarchus of Samos and the diameters of the Moon, Sun and their distances. MathJax reference. 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 ), but Eratosthenes needed to know that it was immensely farther than that. So everywhere is close to the centre of the moon's orbit. 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. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. "And the Sun is further still. What is the equivalent to Scientific Linux Users as a professional trouble shooting email list for Ubuntu? I don't know if one is dependent on the other though. It is unlikely that Eratosthenes assumed the Sun was infinitely distant, since he apparently also estimated the distance to the Sun himself. Co-ordinates: Astronomy > Earth, Moon, Sun > Earth. 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. At half moon, the sun seems to be at $90^\circ$ to the moon. Why does \renewcommand error if the command does not exist?

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