Longititude difference measured how? Guess the nominal distance is too fuzzy to worry about great-circle hypotenuse vs long-side error?
Despite numerous errors, Eratosthenes' calculation was off by only 0.16%.
By the way, it was he who developed the system of latitudinal and longitudinal lines to map the world.
By the way, it was he who developed the system of latitudinal and longitudinal lines to map the world.
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I've done some research! 😎
From Wikipedia: "Eratosthenes, in the 3rd century BCE first proposed a system of latitude and longitude for a map of the world. His prime meridian (line of longitude) passed through Alexandria and Rhodes, while his parallels (lines of latitude) were not regularly spaced, but passed through known locations, often at the expense of being straight lines." https://en.wikipedia.org/wiki/History_of_longitude#:~:text=Eratosthenes in the 3rd century BCE first proposed,at the expense of being straight lines.
Eratosthenes knew that Alexandria was north of Syene and had to assume it was due north for his calculation.
The longitude of Alexandria is 29.9
The longitude of Aswan (Syene) is 32.9
The discrepancy is just one of the errors in Eratosthenes' calculation.
Eratosthenes did not take both measurements on the same day! The astronomer took a measure of the solar angle in the town of Syene in southern Egypt on the summer solstice. He then walked to the town of Alexandria in northern Egypt and carefully measured the distance along the way and measured the solar angle again on the summer solstice in the following year.
From Wikipedia: "Eratosthenes, in the 3rd century BCE first proposed a system of latitude and longitude for a map of the world. His prime meridian (line of longitude) passed through Alexandria and Rhodes, while his parallels (lines of latitude) were not regularly spaced, but passed through known locations, often at the expense of being straight lines." https://en.wikipedia.org/wiki/History_of_longitude#:~:text=Eratosthenes in the 3rd century BCE first proposed,at the expense of being straight lines.
Eratosthenes knew that Alexandria was north of Syene and had to assume it was due north for his calculation.
The longitude of Alexandria is 29.9
The longitude of Aswan (Syene) is 32.9
The discrepancy is just one of the errors in Eratosthenes' calculation.
Eratosthenes did not take both measurements on the same day! The astronomer took a measure of the solar angle in the town of Syene in southern Egypt on the summer solstice. He then walked to the town of Alexandria in northern Egypt and carefully measured the distance along the way and measured the solar angle again on the summer solstice in the following year.
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Thanks for the research. Methinks he "knew" the answer and fudged his data to fit within 1/600. That 3-degree longitude difference errs by lots more; and walking measure??
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I do not see how Erathosthene could know Sienne and Alenxendria are about at the same longitude.
I think that was a wild guess from him, until one gives to me the way he could be sure of this fact.
I think that was a wild guess from him, until one gives to me the way he could be sure of this fact.
Was it his ability to estimate direction that you doubt?
Eratosthenes would estimate direction using the eight principal winds: https://en.wikipedia.org/wiki/Classical_compass_winds
He only had to ascertain that Alexandria was approximately north of Syene.
Apparently, the error introduced by even a large west-east offset is negligible.
My disquiet on Eratosthenes (of Cyrene, in what is now Libya not far from Benghazi) was that he apparently read a script in the Alexandria library (by someone else) about the sun shining down the well vertically at Syene (Aswan, Egypt) on June 21st. But he was the one who obviously put 2 and 2 together that the Earth must be curved. Thus set out to find how far Syene was from Alexandria around 240 BC. The rest is just geometry. I recall they knew about Sines and Cosines and all that. 7/360 = about 1/50.
Given the advanced state of Greek mathematics at the time, he must have gone for a spherical solution. I would think the Greeks knew quite a lot about direction and distances if they were to navigate ships around the 1000 Greek city states. Usually the Great Bear or Ursa Major was the indicator of North, the Noonday Sun South and so on, and to East Sunrise, and to West sunset.
I did an estimate of the Pole Star in antiquity. It does in fact move around over 26,000 years as we now know.
There is great military and commercial advantage in accurate navigation. The Greeks must have been good at this.
Rather shocking that we had to wait for Tycho Brahe using his eyes, and Galileo his telescope nearly 2000 years later to get back to this brilliant standard of scientific inquiry. 😡
Given the advanced state of Greek mathematics at the time, he must have gone for a spherical solution. I would think the Greeks knew quite a lot about direction and distances if they were to navigate ships around the 1000 Greek city states. Usually the Great Bear or Ursa Major was the indicator of North, the Noonday Sun South and so on, and to East Sunrise, and to West sunset.
I did an estimate of the Pole Star in antiquity. It does in fact move around over 26,000 years as we now know.
There is great military and commercial advantage in accurate navigation. The Greeks must have been good at this.
Rather shocking that we had to wait for Tycho Brahe using his eyes, and Galileo his telescope nearly 2000 years later to get back to this brilliant standard of scientific inquiry. 😡
Yes, Steve, which star is our "north star" changes over the centuries due to the precession of Earth's rotational axis, i.e., the Earth wobbles like a spinning top.
Vega, shown in the above diagram, was our "north star" around 12,000 BCE.
And there is a link back to Eratosthenes who was the first to calculate the Earth's axial tilt.
Your star map shows that Thuban was our "north star" some 5,000 years ago when the Egyptian pyramids were being built.
Larry Niven imagined a ring with a radius of 93 million miles (the distance of the Earth from the Sun) with the Sun placed at the centre.
With an area three million times that of the Earth, the Ringworld could support trillions of people!
By rotating, the Ringworld could simulate Earth's gravity (if accelerated up to nearly 3,000,000 miles per hour!).
The image below shows how "sunshades" would have to be deployed between the Ringworld and the Sun in order to give its inhabitants the experience of night and day instead of being bathed in perpetual sunlight.
More here: https://www.popularmechanics.com/space/deep-space/a11183/could-we-build-a-ringworld-17166651/
Dennis E. Taylor hoop Heaven's River. BTW that's the name of a Silk Road city on the east bank of the great basin which sits atop a huge underground sea formed (I conjecture) by a micro-comet 5000 years ago hence the global Flood myths and what I dub the ancient archaeological divide: no site spanned 5kya. Taylor's earlier Bobiverse novel was possibly inspired by Banpo Half-Mesa site downstream from this Tianshui Heaven's River. As for the Mediterranean Sea, a land-bridge possibly connected Greece and Turkey directly (DNA migration evidence) but collapsed and/or was innundated by the Flood.
We are wandering a long way from "Gravity" here, but it's all Science or "Philosophy" I suppose... 😎
The Mediterranean Sea formed about 5 million years ago, IIRC, when the Pillars of Hercules formed and let the Atlantic in.
Alexandria seems to have been a good place to do good work in unravelling the mysteries of the World or Universe:
Eratosthenes had a good library and a good observation platform, The Pharos of Alexandria, nearby for his calculations:
Half a Stade (ca. 100m or half a furlong) high, which means you can see it from about 20 miles away in a trireme, I suppose, though I haven't calculated that.
Had a mirror to reflect the Sun in daytime, and a furnace at Night. Which is clever IMO.
Looked like this in 1780:
Now an interesting tourist destination after considerable reconstruction following Earthquakes around 1000AD:
There is a largely surviving Lighthouse from Roman times in A Coruna in Galicia, Spain, The Tower of Hercules:
1/3 of a Stade high. Called "Finisterra" or "The End of the World". Allegedly you could see Green Ireland from this place, which is just plain fanciful to my mind.
Forgotten where I am going on this! Ah yes, The Pole Star, historically:
Must have been an interesting sky about 14000 BC. Lots of bright stuff due North, Deneb and Vega and the Milky Way there.
I will hold back on Gravity 'til I have finished the Susskind course on Classical Mechanics. Still on circular orbits ATM.
You know, r double dot (acceleration) an' all that. Most interesting. Hadn't really thought about it.
The Mediterranean Sea formed about 5 million years ago, IIRC, when the Pillars of Hercules formed and let the Atlantic in.
Alexandria seems to have been a good place to do good work in unravelling the mysteries of the World or Universe:
Eratosthenes had a good library and a good observation platform, The Pharos of Alexandria, nearby for his calculations:
Half a Stade (ca. 100m or half a furlong) high, which means you can see it from about 20 miles away in a trireme, I suppose, though I haven't calculated that.
Had a mirror to reflect the Sun in daytime, and a furnace at Night. Which is clever IMO.
Looked like this in 1780:
Now an interesting tourist destination after considerable reconstruction following Earthquakes around 1000AD:
There is a largely surviving Lighthouse from Roman times in A Coruna in Galicia, Spain, The Tower of Hercules:
1/3 of a Stade high. Called "Finisterra" or "The End of the World". Allegedly you could see Green Ireland from this place, which is just plain fanciful to my mind.
Forgotten where I am going on this! Ah yes, The Pole Star, historically:
Must have been an interesting sky about 14000 BC. Lots of bright stuff due North, Deneb and Vega and the Milky Way there.
I will hold back on Gravity 'til I have finished the Susskind course on Classical Mechanics. Still on circular orbits ATM.
You know, r double dot (acceleration) an' all that. Most interesting. Hadn't really thought about it.
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The"Bobiverse" series of novels is Sci-Fi I haven't yet read - sounds interesting!
"Bobs" are self-replicating von Neumann probes sent out to explore the galaxy.
https://en.wikipedia.org/wiki/Self-replicating_spacecraft