ELI5 version. A guy in ancient Egypt, a clever guy called Eratosthenes had some ideas to calculate the circumference of the earth. In the end, he used the position of the sun, the length of shadows at a certain time and date and some known distances to estimate the circumference.
It's worth noting that even then, they knew the earth was a sphere. Nobody really thought the earth was flat.
Nobody really thought the earth was flat.
And this gets at a very common misconception/lie that permeated my youth. NOBODY thought the earth was flat. At least, not anyone with a modicum of education or navigation experience. Maybe your normal peasant working on a farm wasn't really thinking about that. It's something we've known for thousands of a years. And no, Columbus did not prove the world was round. Columbus was a fool who thought he could travel west to get to the Indies more quickly because he thought the Earth is significantly smaller than everyone else (correctly) thought it is. He just got lucky and stumbled across a continent along the way.
Everyone laughed at Columbus because they knew there was no way to make it across both the Pacific and Atlantic with the naval technology of the time. He got really lucky there happened to be an entire continent there.
He may be a piece of shit but he was no fool and was actually quite the talented sailor. They navigated using dead reckoning back. Look it up, not exactly easy.
Columbus was not a 'fool', he made multiple successful voyages over the years and was responsible for the lives of thousands of men on his journeys.
Columbus could not get funding for his journey because everyone who did their due diligence realized he had undervalued Earth's equatorial circumference and he would not be able to carry enough supplies for the actual westward voyage from Europe to India on a carrack and two caravels. The King of Portugal rejected his request twice (first on the bad math grounds, second on the "we already control the long way there around Africa" grounds). Queen Isabella of Castile finally did agree to pay for it (partially so the French wouldn't hire him), and it was sheer luck that the Caribbean islands were where his map showed land would be.
Yeah. Piece of shit. But a talented sailor
Great episode of “short history of” podcast on this topic
NOBODY thought the earth was flat. At least, not anyone with a modicum of education or navigation experience.
Explicitly wrong. https://en.wikipedia.org/wiki/Flat_Earth#East_Asia
At different times, the most populous country in the world but almost always within the top few. And apparently that's NOBODY to you.
What you really meant was nobody that you cared to think about, and a large chunk of the global population didn't matter to you.
I didn’t realise until recently the flat earth shit is only from the last couple centuries, can’t remember the reason why it started. Think it was evolution related, not sure.
It was evolution-related. Starting in the 17th century, various intellectuals dunked on their predecessors by claiming people in the past believed in primitive ideas like a flat earth. This led to a narrative that the Catholic Church suppressed the concept of a round earth, which Protestants gladly amplified.
When Darwin's ideas on evolution sparked a debate in the 19th century, some opponents went with the line "scientists were wrong about a round earth and they're wrong about this."
I don't understand why anyone would ever think the Earth is flat. The sun and the moon are spherical so it would make sense to assume that the Earth is too.
Plus, people living on coastlines could see ships dipping below the horizon.
If you live inland and have no education beyond how to work a farm, the shape of the earth is not obvious. The horizon of a flat Earth is only a few arc-minutes above the horizon of a round Earth. With hills, trees, buildings, and everything else in the way, it would be impossible to tell the difference.
But you're right, you have to go very far back before educated people didn't know that the earth was round. Even more convincing than the shape of the sun and moon is that lunar eclipses were always circles. Lunar eclipses happen twice a year, so there would have been plenty of time for astronomers to notice.
The sun and moon are disc-shaped. You can have a (relatively) flat disc. Especially since we only ever see one side of the moon.
Have you ever had a coin? That's a flat disc that is not a sphere.
By your own logic, it would make sense to assume the Earth is also a flat disc.
Except we don't have evidence of flat disc shaped astronomical objects being in orbit. No one has ever seen the "thin side" of the moon or any evidence that the celestial objects have a thin edge.
Plus, if celestial objects were disc shaped, wouldn't they look less round and more elliptical depending on what position you're observing them from the Earth?
Now the discovery of heliocentrism taking a bit longer, that I get because it appears that the sun moves around the Earth. But seeing that the celestial objects are spherical should be obvious enough just by looking at the sky.
The fact that NO ONE has posted the Carl Sagan video already is extremely disappointing to me.
Thank you! The moment I saw the question I was expecting this to be the first result.
Man was Carl Sagan great at explaining complex topics.
This entire thread is just people posting that video and also saying "they did trigonometry with shadows" which isn't an ELI5 answer at all.
Carl Sagan's explanation is pretty acceptable as an ELI5, and I made this post like 5 hours ago when it WASN'T full of this answer. Welcome to the party.
ELI5 isn't for just posting links to the answer. It's for people to actually explain it.
Bruh....Carl Sagan can explain it better than literally anyone here. You're being purposefully combative for absolutely no reason. Give it a rest.
What part of doing trigonometry with shadows isn't ELI5? Just asking for insight.
One of the first was a greek guy called Erathosthenes.
As the story goes, he lived in Alexandria on the northern coast of Egypt. One day he read that on the longest day of the year, at the first cataract of the nile (so up river from where he was, and almost exactly south), a stick that was stuck into the ground vertically would not cast a shadow at noon - the sun being exactly overhead, thus no shadow.
So, on the longest day of the year, he stuck a vertical stick in the ground in Alexandria and noticed that it did cast a shadow. He measured the angle of the sun - not vertical in Alexandria. Then he sent a servant from Alexandria to the first cataract of the nile and told him to count his steps on the way there, and again on the way back.
This gave him the distance along the curvature of the earth, and together with the angle he had measured, he could then quite easily figure out the entire circumference.
A very simple method, but he was only off by about 4%.
They looked at the difference in shadows of two places on the same longitude. Since they knew the distance between them, based on the angle they could estimate the circumference.
Check these two videos. They explain this perfectly
Should be higher up. These are wonderful.
This is one of the best « science explanation » documentary I’ve seen. They are perfect
Carl Sagan did an amazing explanation of this on the old Cosmos show. It is on YT and worth checking out. Man, he was such a great explainer.
They dug a deep well in this one town, and realized that at a certain time of year, at noon the sunshine went all the way to the bottom, meaning the sun was nearly exactly overhead. Then this dude found a town north of that town, and used the shadow of a tall vertical pole to figure out that when the sun was directly over the first town, it was about 7 degrees from being directly over the second. Knowing that the sun was insanely far away, that meant that two perfectly vertical poles through the towns would be roughly 7 degrees off each other, aka ~2% of a circle. The two towns were about 500 miles apart, which meant that ~2% of the earths circumference was about 5000 stadia, so the whole circumference is about 250,000 stadia. He was using a unit of distance that we don't have an exact conversion for, but the estimated conversions place his estimation at ~24,600-25,000 miles. Modern measurements place the circumference at 24,900, meaning that at worst he was a couple percent off.
This made the most sense but it’s the most complicated hah!
https://www.youtube.com/watch?v=YdOXS_9_P4U
One guy noted that on a certain day (and only that day) you could see the sun in the bottom of a well at noon in a specific town. so someone else figured the sun must be directly overhead of that well at noon that day, so on that day at noon, he measured exactly where the sun was at his home town, and measured the distance to the well.
Then its just a bit of trigonometry.
Ancient greece did it by measuring the length of the Shadows of two big obilisks in two cities at exactly 12:00.
They knew the distance between the cities, and they knew how long the shadows of the tall obilisks were, and by this they could not only calculate the size of the earth but also proved that the earth is a round ball.
And with just a pen and paper and lots of footwork, they came super close to the actuall size of the earth.
Nitpick: that didn't prove the earth is a round ball. They already knew it was. On its own the same measurements could be used to calculate distances on a flat plane.
However, when you do this experiment in multiple locations, then you'd see that all the individual measurements only make sense on a globe.
Not sure what you ment by the first paragraph, but on the flat plane all the angles would be the same what distance are you talking about there?
Assuming a flat plane, those measurements could find you the distance to the sun. Which works when it's a stand alone measurement. But when you do it in lots of places, the numbers don't make sense. The sun would by X distance above the ground in one calculation and Y in another.
The angles wouldn't be the same - they'd depend on the relative position of the sun
Relative to what? The Earth is so far from the Sun that all the rays falling on the Earth on the flat surface at that distance would be parallel, and that means all angles would be the same. The earths angular size from PoV of the sun is less than 0.005 degree. If Earth were flat you can measure angles of the sunlight at the cities tens of thousands km apart and they would still be the same.
You assume the model of a massive sun millions of miles away with rays coming down parallel. In the (idiotic) concept of a flat earth, the sun is much smaller and much closer and thus non-parallel rays. If you assume that is the case, you can use basic trigonometry to measure the distance to the sun with the measurements Eratosthenes did. It's just a simple right triangle.
However, if you take additional measurements at different points, the numbers stop making sense. The calculation in one place would show that sun is, let's say 50 miles above the surface of the earth, while using another further north at the same time would show the sun being, say, 20 miles above.
Which is why Eratosthenes's experiment didn't prove the earth is a globe. He only had a single triangle. He was, correctly, assuming the Earth is a sphere and was using that one triangle to measure its size. If he had done multiple measurements at points significantly far apart, THEN it could show that a flat earth is not possible.
"Which is why Eratosthenes's experiment didn't prove the earth is a globe."
At the scale of his experiment (800km) between cities the Sun has to be only 5,000km away and 50km wide for it to work on a flat surface.
Both Eratosthenes and Aristarchus of Samos 20 years before him did calculations on the distance to the Sun and while not very accurate they both knew the Sun was significantly far enough away and for that matter much further than 5,000km.
So, while Eratosthenes wasnt out to prove a round Earth it still the case that his only 2 options were:
A. Near Sun/Flat Surface
or
B. Far Sun/Curved Surface
and because of that even 2,265 years ago Eratosthenes could disregard option A as a possibility which leaves only B.
Geometry mostly. And of geometry mostly trigonometry (the study of triangles). You can break down pretty much any shape into triangles, then use the lengths and angles you know to figure out more lengths and angles.
Eratosthenes figured that the Earth was a sphere, found a spot where the sun shone directly down a well at noon, then used the the length of a shadow of a stick of known length at a point north of that well to figure out the circumference of the Earth to within 1% of the actual circumference. It's beyond ELI5 but fairly basic trigonometry. This picture from the above article gives the method pretty well
Doesn’t even need triangles. If you go 400km north of the well with no shadow, and measure that (say) the shadow is at 3.6° off vertical, then (as there are 360° in a circle) you know that 400km is 1% of the way round.
The most accurate way was measuring shadows on specific days (solstice or equinox usually, but with enough knowledge any day will work).
This number is off the top of my head, but I believe the accuracy was about 99.3 percent accurate in the 5th century BCE, and 99.1 percent as far back as 15th century BCE or even earlier.
There is a lot of math involved, and part of the reason they didn't get even more accurate numbers is because they had no way to know the earth ISN'T a perfect sphere but is instead an oblate spheroid (very slightly longer diameter around the equator than the diameter from North Pole to South Pole), but that little discovery took modern technology to discover.
First you need to know the rough distance north/south between two places that are significantly far from each other (say, 100 miles).
One day a year when the sun is at its highest point in the sky in one spot, the sun will be directly overhead. On that same day in the other place when the sun is at it's highest in the sky, it will still cast a shadow. Find a deep hole or a tall building with straight sides, and you can measure the angle of the angle of the shadow.
Now you can do some fun math to figure out how big a curved surface would need to be to for the light to come in at 90 degrees at point A and at the angle found at point B when they are X distance apart.
One of those places has to be inside the Tropics. That is the only place where the Sun casts no shadow.
In really simple terms if you stick a post in the ground and wait for high noon (when the sun is exactly halfway across the sky) you will see one of two things, either there will be no shadow because you are directly under the sun or there will be a shadow because the sun is at an angle to you.
The place where the post casts no shadow is 0° because the sun is not at an angle to you so that where you start, then you walk some random distance to a place where there is a shadow and you can do some math to find out what the angle of the sun is by using triangles, for example if the post is 1 meters tall and the shadow is 1 meters long then you know the sun is at a 45° angle to you. A full circle has 360° in it and 45 is 1/8 of 360 so take the distance of the two posts and multiple it by 8 to get the earths circumference.
Take two cities kind of far away
Where sun at noon on same day
Angles
Math
Round number for round planet
Measured? - I don't believe anyone ever has. Would be an interesting story, for sure.
Calculated? As far as we know, Eratosthenes of Cyrene was the first to do so, after hearing of a town in Egypt, where the sun was directly over a well at summer solstice, casting its rays directly down into it, with no shadows. - He then measurered the angle of the shadow cast by a stick at the same time and date in Alexandria to about 7.2 degrees, which just so happened to be 1/50th of a full circle of 360 degrees.
He logically then reasoned that the distance between that town (Syene) and Alexandria must be 1/50th of the Earth’s circumference, and multiplied the estimate of the distance by 50, to calculate the full circumference of the Earth to either 39 000 or 46 000 (we aren't sure, as we don't have the exact definition of the unit he used for distance, - a "Stadia").
Pretty decent, as we have a number today, of 40 075 km around the equator.
Calculated vs Measured. I feel you. Even though the terms are not interchangeable they often are used in conflicting context.
IN Sky and Telescope of September, under the heading “Saluting an Astronomer”, Joseph R. Habes has an article which describes the method adopted by Eratosthenes for measuring the circumference of the earth.
https://www.nature.com/articles/152473a0
The first person to determine the size of Earth was Eratosthenes of Cyrene, who produced a surprisingly good measurement using a simple scheme that combined geometrical calculations with physical observations.
https://www.aps.org/apsnews/2006/06/eratosthenes-measures-earth
An ancient Greek astronomer named Eratosthenes was the first man to measure the size of the Earth accurately. His method was very simple: he measured the angle made by a shadow cast from a vertical stick in two different cities on the same day and time.
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Astronomy_for_Educators_(Barth)/05%3A_Measuring_and_Mapping_the_Sky/5.04%3A_Measuring_the_Earth_with_Eratosthenes/05%3A_Measuring_and_Mapping_the_Sky/5.04%3A_Measuring_the_Earth_with_Eratosthenes)
The method of measuring the Earth's circumference was carried out in Alexandria, Egypt for the first time in the 3rd century BC. Eratosthenes was astronomical knowledge, philosopher, mathematician and director of the Alexandria Library.
https://ui.adsabs.harvard.edu/abs/2018EGUGA..20.5417K/abstract
I'm fairly sure no one has ever actualy measured the circumference of the earth directly. like no one has used a measuring stick, survey wheel or such and ran it around.
we have measured more practical things, like the first folks measure the shadow of a stick at multiple locations, and used that measurement to calculate the circumference of earth.
Even today -- we could drive/sail or fly aroung the earth, and use GPS... which would get us a measurement of position via time differences, and with quite a bit of math, calculate the distance traveled.
but at it's most simple. we've never measured the circumference. we have calculated it quite closely -- more closely than we could measure.
Do we need to know how far the sun is for the calculation? When/how did we know how far away the sun is?
You do not need to know the distance to the Sun beyond "really far."
There were some estimates of the Earth-Sun distance at the time Eratosthenes was around, but they weren't that accurate, given the poor precision of measuring equipment of the age.
We didn't have a really precise figure (within 5%) until 1761, when the transit of Venus could be measured.
The sun is far enough away that the rays hitting the earth are almost parallel. You can get very close by assuming the sun is at an infinite distance.
Eratosthenes used this method:
From these information he could use his knowledge of trigonometry to calculate the circumference of Earth. It was very rough approximation, as the distance between cities was mainly measured by steps before moder geodesy came in. But this is the first known instance of doing such a measure.
For a 'very rough' approximation, it was not too far away - error margin of less than 1%.
There was a certain amount of luck there though. He made two errors that happened to cancel each other out.
Not to disparage Eratosthenes.. Even getting within 10% would have been remarkably accurate for the time.
Can you please tell me what those two errors were?
Edit: Because it sounds like a pretty easy calculation, by modern standards of course. I'm sure it was far more difficult back then
The errors didn't have anything to do with the math. They were errors in measuring reality accurately.
Ahh, I make those errors all the time
Right there with ya, brother.
He assumed the cities were directly north/south of one another and that one of the cities was on the tropic of cancer
He was slightly off by a bit in both and those cancelled each other out
Must have been such a weird time to be a scientist.
Sheep farmer: "Hey Eratosthenes, what are you doing today?"
Eratosthenes: "I'm going to measure shadows in different cities to try and approximate the size of the earth."
Sheep farmer: "And what will you use that information for?"
Eratosthenes: 🤷
Sheep farmer: "Well, how will you know if you're right?"
Eratosthenes: 🤷
I love it lol
I’m going to steal this, and use it at parties to make people think I’m smart.
I’m a bore otherwise, so I apologize, and thank you.
Errors-crossed-enes
Sensational. This made the internet worth it today. Thank you
And thank you laserdicks.
I think it was the distance between the 2 cities and he thought Syrene was on the tropic of Cancer rather than slightly north.
That's really funny honestly
Also worth noting: people deliberately exploit this kind of thing to make predictions more accurate all the time. Whenever you have multiple imprecise measurements, if the errors in each are independent of each other, the more data points you have the more likely it is that overall they more or less cancel each other out.
If I measure the temperature with two shitty thermometers and average the results, that’s slightly more reliable than using either one of them individually. If I measure the temperature with 100 shitty thermometers and average the results, that’s going to be really accurate. That is, assuming they’re not somehow all flawed in the same way, in that case the average only amplifies their shared flaw(s).
The wisdom of crowds. Ask one person to guess a factual number (distance from New York to Chicago for example) and they will probably be wrong. Ask more people and the average will start to be more accurate, as some people will guess under and some over
So, like I guess 1000 miles
ONE MILLION MILES
Negative a million.
But also… 875?
In my country we have a kind-of state lottery that instead of random numbers, you try to predict the result of upcoming soccer matches. One time, at school, we were each given a ticket and asked to play.
I've never had any interest in soccer, but I was tasked to retrieve all the tickets. I did so, and only then I filled mine, with the average of all the others. I got the best score of the class (still won nothing)
That's not the same thing. Assuming "shitty" refers to just large error bars, then you're just using statistics to compensate for that. What was described here was cancelling out two systematic errors. If you're measuring the gas mileage on your car and you know your odometer overestimates your distance traveled and your fuel gage overestimates the fuel used, then the fact that you're dividing the two means that two overestimates cancel out, resulting in an overall smaller systematic error.
Fun fact - the T-Test, a mathematical test to determine if deviations of a small sample are statistically significant, was invented thanks to beer.
Specifically, Guinness beer. They wanted to expand sales globally but faced a simple issue: the raw ingredients (hops, malt, barley, water, etc.) could change constantly but they wanted the final product to always taste the same.
So along comes this chemist named William Sealy Gossett who determined what the optional composition is for each ingredient and the sources for the best ingredients.
However, that still leaves them with a different issue. You can't just test every single ingredient in each batch. That would be very impractical. Instead they tested samples and looked at the average.
And yet that presented them with another issue. If the samples are off from their desired composition, how do they know if that's bad? They could have just selected a poor sample. If the hops should be, say, 6% soft resin, is it bad if the sample averaged 7%?
What that meant, he realized, is that you need to know the likelihood that a sample from a good batch would have a bad result. That's where the T-Test came in: if you knew the expected standard deviation for the composition, you could determine what are the odds that a small sample would return values within a certain range and if that meant the batch of ingredients would likely be okay.
Here's a more in-depth article.
So he really did say hold my beer...
Underrated
This was a fun fact - thank you! I always wondered where the T-test came from
Presumably even then it wouldn't actually amplify their shared flaws, simply average them. You wouldn't be any worse off ~50% of the time.
Right, "amplify" wasn't the best word choice there; I meant that if the same systematic error is present in many/all of them then when you average them, instead of final estimate going from [low accuracy / low confidence] to [high accuracy / high confidence], it goes to [low accuracy / high confidence], which is arguably worse than where you started.
Using 100 bad thermometers without systemic bias to find a more accurate approximation of the true temperature isn't an exploit, that's just good measurement. That's like saying it's an exploit to use a large sample size in a study.
Disparage Eratosthenes at your own peril.
That's not luck, in statistics it's called compensating errors.
Per Law of Large Numbers, as measurements increase, the average converges toward the true value due to error cancellation. Central Limit Theorem also plays a role in this because the distribution of averaged measurements approaches a normal curve, centered on the true value.
I don't think anything you said is relevant...
Some types of errors tend to do that. I seem to remember reading that the Great Trigonometry Survey of India, which measured the country from one end to the other, ended up only a few inches adrift at the far end. But for a mere two to do it, yes, it's luck.
As rough as it was, he was still so close we could call it correct. He estimated 40,000 km, actual value is about 40,075km.
Interesting. Reminds me of the reason surveyors used to say Mt Everest was 30,002 feet - the initial surveys came in at exactly 30,000 feet and they were afraid people would think they were rounding off. So they said 30,002 instead, figuring that it wouldn’t change much in practical terms but gave them some extra credibility.
Me writing out estimates.
$30,000 🤚
$30,052.34 👈
In Healthcare
BP 120/80 🤚
BP 124/80 👍
In this case, it's the opposite. They measured it in a measurement that pre-dated Metric. The kilometer was later defined to be 1/10,000th the distance from the pole to the equator. (1/4th the total circumference). Later, after we set all weights and measures, we discovered the earth was slightly more than that, but it wasn't worth redoing the entire metric system over.
28000 iirc
Wikipedia says that it was 29'000 feet, so you're equally right and equally wrong - assuming Wikipedia is correct.
Yup. Another fun fact is that Mount Everest (pronounced ever+est) is named after the British Surveyor General of India George Everest (pronounced eve+rist).
the funny thing is that it changes every year due to erosion
I can't recall off the top of my head which was more significant to Everest's height, erosion or the continuing uplift of the Himalayas.
IIRC it's growing faster than eroding, with a balance of a few mm a year. I remember reading that Everest is basically at a maximum height possible given the earth gravity and rock/soil composition, so while it is growing, it's unlikely to grow significantly.
Very neat. I just like the fact that if you go above 20,000 feet, you're slowly dying and can't live there permanently. So my goal is base camp :p
Interestingly, the French defined the meter such that the earth has 40,000 km circumference and they were off by the same amount even though they used much more sophisticated distance measurements in the 18th century.
Here’s Carl Sagan explaining this exact topic
Fun side note: Notice how much Agent Smith’s voice and cadence sounds like Carl Sagan.
"Billions and billions, Mr. Anderson..."
Edit:
Fun fact, there is a tongue-in-cheek measurement unit known as a Sagan, which does not have a determined value but instead a floor, set at 4 billion. The idea is that "billions" is plural, so at least 2, and "billions and billions" is adding two of those together.
Fun fact 2: Sagan never actually said "billions and billions" in the entire course of the Cosmos series, and was mildly annoyed when the phrase got popularized due to Johnny Carson on a Tonight Show skit. Nonetheless, he eventually softened, and the last book he wrote, published posthumously, was titled "Billions and Billions."
Love me a fun fact or two. Cheers.
Also Trumps favourite book title. He doesn't read the books of course.
Here's what I've never understood about this:
He knew the sun was directly overhead in Syene. Noon.
He measures the shadow angle in Alexandria.
My question, is when? How did he know to measure the Alexandria shadow by Syene's noon? How does he know WHEN during the day to measure in Alexandria, since Syene is 5000 Stadia away, with no instant communication or way of marking he time, that could coordinate the time in the two cities?
What I conclude is that in Alexandria the sun was never directly overhead, and he measured when it was the shortest.
Would love someone to verify this or correct me
He assumed that both cities were at the same longitude, and that is almost correct.
Right, and suns rays parallel, and nearly canceled out
Alexandria is outside the Tropics, therefore the sun is indeed never directly overhead. Technically it is also never directly overhead in Syene because the tropic circle is still a little bit further south, but it was close enough that on the day of summer solstice there was no practical difference.
Yes. Outside the Tropics, noon on the day of summer solstice is the moment when shadows are the shortest they can be. For Syene, it was known that "the shortest they can be" is actually 0. So when it was summer solstice noon in Alexandria, when shadows were as short as they could get, Erastothenes knew that in this very moment shadows don't exist at all in Syene.
That is, if we disregard the fact that they are not exactly on the same longitude, and therefore noon happens ca 12 minutes later in Alexandria than in Syene. But that doesn't make a difference; the sun's position relative to the earth's equator doesn't meaningfully change in that time. What's more relevant is that due to this difference in latitude, the distance between the two cities isn't equal to the distance between their latitudes. Furthermore, as already mentioned, the length of shadows in Syene isn't exactly 0.
Anyway, I don't think we know for sure which of these factors Erastothenes was aware of, and whether he somehow factored them in, because the only source we have is a later author who explicitly admits that he's only giving the ELI5 of what Erastothenes actually did.
Finally, thank you person. The fact that the shadows are not zero in Alexandria at noon, omitted every time I've read this in 30 years baffles me. I appreciate your explanation, and shall rest easy now.
Eratosthenes used existing survey data compiled by professional bematists (specialized surveyors who measured distances by pacing (and were trained to take even steps)) from the libraries in Alexandria.
He already knew that in Syene (modern Aswan), the sun was directly overhead at noon on the summer solstice, because it illuminated the bottom of a deep well and cast no shadow (it was a well-documented local phenomenon).
By measuring the angle of the shadow cast by a gnomon during the summer solstice in Alexandria, it was possible to compare the results and calculate the difference in latitude between the two cities.
From there, it just took a little more math to estimate the circumference of the Earth.
All that I understand. But how does he know when, when noon is local?
Let's say watches exist back then. Exact noon at Syene is 12:00 pm, and no shadow found in the well.
E's watch in Alexandria reads noon, and he knows NOW, this minute, not 5 min before, or 5 min later, when his watch reads noon, that's it's now time to measure.
Now remove the watches, how does he know WHEN to measure?
What's to stop him from measuring at 12:05, or 11:55, and since he's off on time, the whole thing doesn't work?
Edit : I see now, you say 'angle of gnomon,' I should have understood that as a non zero shadow in Alexandria. Thank you.!
People are going to talk about how close he got... but in actuality his measurement was not very good. Here are a bunch of things you need to know.
We do not have the original work, it was lost to time. We only have a simplified version of his worked printed by another author.
The measurement was recorded in stadion (a unit of measurement of the time). This measurement was equal to 600 Greek feet, however this resulted in many variations on the length of a stradion in Greece, with each region having a different version. The end results is a stradion could be between 157M and 209M. The "within 1% accuracy" statement is assuming the best fit. The measurement could have been off by 30%, we don't know.
He believed that Syene (one of the measuring sites) was directly south of Alexandria and located on the Tropic of Cancer, but this is off by 3 degrees. He also used an estimated distance between Alexandria and Syene, which was wrong. Luckily these inaccuracies mostly cancelled each other out, but that was just from dumb luck.
Eratosthenes did a lot of really good work and got very far for his time. He was a good scientist. But the 1% accuracy thing is essentially a myth formed by ignoring details and choosing the best interpretations for this narrative.
I even believe that some scholars took the Eratosthenes calculation to estimate stadia. Which would seem to have a bit of a recursive problem.
Finally someone pointing this out, I was reading the replies mentioning the 1% error and shaking my head, but not having the willpower to bring this out. I second this 100%. Still he got a great result considering he was using the shadow casted by a stick.
Carl Sagan tells this story quite eloquently on the YouTubes...
This is a part of what is called the Celestial Ladder.
It was also off because the Earth isn't a perfect sphere, it's wider at the equator, but again, it was really freaking close.
This is just badass, what a chad.
What blows my mind is everything else that had to come before. Someone noticed there’s no shadow one day a day, word about that was exchanged with other scientists in other cities
It has been going on long enough to predict the next time it would happen.
Presumably this required some notion of time of day and synchronising them too?
Dumb question... how did he know what time "noon" was in Syene while he was in Alexandria? I didnt think they had that level of timekeeping back then.
He didn’t need an exact time in the sense of a clock. It was based on observation of the sun’s position. So it wasn’t, what was the shadow at a specific time, it was, what was the shadow at a specific observed position if the sun.
But it was the position of the sun in Syrene while he was in Alexandria right?
EDIT: Also, funny running into you here!
The position of the sun overhead is the same time, if they’re on the same line of longitude, which he mistakenly believed Alexandria and Syene to be (they’re off by a little bit). That was the point of using the two cities - the sun reaches its peak position in both at the same time, thus solving his inaccurate time-keeping problem.
Also: HA!
Well, he (incorrectly) believed Syene was due south of Alexandria, so solar noon (when the sun is at its highest in the sky) would have been at the same time in the two places.
But the two measurements don't have to be done simultaneously. What you're trying to determine is the angular altitude of the sun at solar noon. So what you can do is plant a stick in the ground, mark the position of the end of the shadow throughout the day, and then go back and measure where it was at its longest. And you can repeat the measurement at a different location, on the same date, next year.
He was able to do the measurements simultaneously because he knew the exact time and day when the shadow measurement to the South was 0 degrees. No shadow means no measurement required and he just had to take his measurement on the Solstice when the Sun was at it's highest.
He knew it was noon when the sun was as high as it would go in its arc in the day, when it had reached its zenith. The time that that occurs is called Local Apparent Noon. The sun is at its zenith at local apparent noon and that is true for all locations along the same longitude- the difference being that the height (angle of sun above the horizon) will be different for every location. So, if two cities are located directly north or south of eachother they will experience local apparent noon at the same time. The observers Syene and Alexandria didn't need to be in communication with eachother, they just knew that if they made their measurements on the same day at local apparent noon it would occur at the same exact time.
Rabbit holes: Sidereal time, Mean Solar Time, Equation of Time, George Daniels' work also his "Space Traveller watch", Longitude (movie starring Jeremy Irons)
At noon the shadow is shortest. So you go out before noon and mark the shadow everytime it has moved away from the previous mark. When the marks start to creep away from the pole, youjust had noon.
better, sit in the shade with a drink and let a slave do he markings.
Carl Sagan explains this in an episode of the excellent series Cosmos.
Hat tip to Carl Sagan for his wonderful video on the subject.