How could Eratosthenes measure the circumference of the Earth?
Upvote:8
Simple.
While the earth moves around the year, the sun seemingly moves around between the Tropic of Cancer (north) and the Tropic of the Capricorn (south). In the north this is begin of summer and the sun reaches the highest point.
The first city where the deep well exists is the city of Syene (now Assuan) which is almost exactly on the Tropic of Cancer, so at almost exactly on June, 21th the sun is almost exactly vertical and the well is lit.
Knowing this, Erastothenes only needed to measure the angle of the sun in Alexandria during June, 21th and knowing that Syene is vertical gets the difference easily. He only need to know the distance between Alexandria and Syene (which must be measured), multiply it with 360 degrees / difference and get the Earth diameter.
Quite genial.
ADDITION: It was asked if it was not necessary to have both cities on the same meridian to get the correct result. While in fact not being on the same meridian does induce an error, this error is neglible because the zenith point of the sun moves with 397 m/s at Alexandria (423 m/s at Syene) in west-east direction. This is supersonic; so even a bigger west-east offset is covered in a short time and an alignment is not needed.
While not necessary, it is quite easy to get the exact geographical north-south direction. Put a straight stick vertical into the earth and draw a circle around it so that the shadow will cross it early and late. Mark the exact points where the shadow touches the circle. Now draw two circles around the points so that the circles intersect. The two intersection points are forming a line which is exactly north-south ! If you do that with stars and a level wall, this will even outperform GPS in precision.
Upvote:17
He synchronised them to the solar zenith.
Eratosthenes knew that on the day of the summer solstice, the sun passed vertically above Syene, which lies very close to the Tropics of Cancer. As the traditional account goes, the sun was directly above a vertical well at Syene, whereas at Alexandria the columns of the Library always leaves a shadow. Either way, he concluded that the sun was 7.2° (1/50) from vertical at Alexandria at its peak.
By making his observations when the sun was highest on the day of the summer solstice, he could be reasonably confident that it was essentially "at the exact same time" to all his practical intents and purposes.
More post
- 📝 Is this conversation factual?
- 📝 Did Greek traders visit the Philippines in the 1st century AD?
- 📝 What is the science behind lead not contributing to the fall of Rome?
- 📝 About the use of the arrow shaped tool in archaological digs
- 📝 What races did Americans classify people into during the 1800s?
- 📝 Was Apollo's birthday December 25th according to the Romans?
- 📝 Were there commercials in the original broadcast of the moon landings, and how much did they go for?
- 📝 What was the role of Scotland during the Hundred Years War?
- 📝 Why was Prince Philip given these specific titles before marrying Princess Elizabeth?
- 📝 At the beginning of English Civil War, why did Parliament take a hard line with neutrals, thereby effectively helping Royalist recruitment?
- 📝 How historically correct is the Maharana Pratap serial?
- 📝 Does Winckler's explanation of Semitic migrations have any merit?
- 📝 Was the concept of religious freedom in the early United States applied to native American faiths?
- 📝 How was nut milk made before blenders?
- 📝 Why were Albanians the only nation in the Balkans who converted to Islam during the Ottoman occupation?
- 📝 Where can I find Japanese oil production figures through WWII?
- 📝 Were Quintidis holidays in the French Republican calendar?
- 📝 What is the equivalent in France of the "Victorian era"?
- 📝 Was there an official name for the bomb detonated in the Manhattan Project
- 📝 When was the first intentional ricochet fired from a naval artillery?
- 📝 Were US decision makers aware of the destructiveness of the Bomb of Nagasaki?
- 📝 Where does the concept of traffic keeping to the "right" side of the street originate?
- 📝 When and where is this probably silver cross with a hollow from?
- 📝 How similar were Finnish and Lenape slash-and-burn agriculture?
- 📝 Were the Barons who pushed King John to Sign the Magna Carta descended from the Normans?
- 📝 Did Admiral Ghormley have access to intellegence reports on Japanese movements prior to the Battle of Savo Island?
- 📝 When did h*m*sexuality become unacceptable in Europe?
- 📝 How young were children left alive in Auschwitz?
- 📝 Why did Austria cede Venetia at the end of the Third Italian War of Independence?
- 📝 What is the longest name chain?
Source: stackoverflow.com
Search Posts
Related post
- 📝 How could Eratosthenes measure the circumference of the Earth?
- 📝 How did they measure speed in the 19th century so they could issue the first speeding ticket?
- 📝 In the Battle of the Coral Sea, how could two Japanese scouts grossly mis-identify two American ships?
- 📝 How quickly could the Roman legions march? How did it compare to their cavalry?
- 📝 Before European influence circa 1600, did any Chinese believe the Earth was spherical, and did they ever try to measure it?
- 📝 How could it be that 80% of townspeople were farmers during the Edo period in Japan?
- 📝 How far away could one be and still see the atom bomb explosions?
- 📝 How could black men serve as officers in the US army during segregation?
- 📝 How much gunpowder could the average Napoleonic ship of the line carry?
- 📝 How could ancient people determine the winter solstice was occurring?
- 📝 How do we measure the adequacy of pre-modern monetary supply?
- 📝 How could nonconformist Protestants be buried in graveyards controlled by the established Church before 1880?
- 📝 During the Middle Ages, how many people could be fed by fishing?
- 📝 How did Farragut know he could get his fleet through the Confederate line of "torpedos" at Mobile Bay?
- 📝 How could the Roman sestertii/sesterces be converted into modern terms (say 2017 US$)?
- 📝 How could the 4/5 devaluation of Franc Poincaré in 1928 end the financial crisis France was going through?
- 📝 How could someone avoid US military service in the early 1950's?
- 📝 How could lower judges ignore the US Supreme Court?
- 📝 How could the USS Maine explosion have been investigated?
- 📝 How could I find the original text of Leonardo Da Vinci's fable "La fiamma e la candela"?
- 📝 How could one understand the essence of Greek mythology and the deep meanings? Understanding the belief system of Ancient Greeks
- 📝 How could a prisoner get lessons to read, write and do mathematics in jail, while innocent people didn't get the basic knowledge in 18th-19th century?
- 📝 How could I determine the value of a a 1921 Yuan Shikai Chinese silver dollar?
- 📝 How could wells back in the day work?
- 📝 how could japan recover very fast their economy eventhough the two bombs were dropped?
- 📝 How could West Berlin had access West Germany/world while the wall was up?
- 📝 How do historians and linguists know how to pronounce the names from non-phonetic scripts?
- 📝 On 1941 Dec 7, could Japan have targeted the Panama Canal instead of Pearl Harbor in a surprise attack?
- 📝 Why did the Confederacy think they could win the American Civil War?
- 📝 Did medieval scholars believe the Earth was round?