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How was the size of Earth first measured? (2015)

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Re: How was the size of Earth first measured? (2015)

#61

Post by extragood »

crazygringo wrote: post #53
extragood wrote: post #50

Earlier quoted context omitted.

This article had one detail that was not included in the video that had always bugged me. Carl says "how could it be .. that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria". That seemingly requires coordination between 2 people across a vast distance and accurate time measurement. I rationalized that it could be accomplished with people at each location, each with a sundi…

> The other unresolved problem for me is that it still requires the assumption that light is parallel i.e. the sun is (relatively) incomprehensibly far away, and that was not established fact at the time afaik. It seems like it very recently had been: https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Ar... There are some Stack Exchange questions that give more background: https://astronomy.stackexchange.com/q…

That is clever! Thanks for sharing these. It's endlessly fascinating to read about how such accurate conclusions were made via simple observation and deduction.

Re: How was the size of Earth first measured? (2015)

#62

Post by extragood »

andrewmutz wrote: post #52
extragood wrote: post #50

Earlier quoted context omitted.

This article had one detail that was not included in the video that had always bugged me. Carl says "how could it be .. that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria". That seemingly requires coordination between 2 people across a vast distance and accurate time measurement. I rationalized that it could be accomplished with people at each location, each with a sundi…

Another way to word it would be "the shortest shadow of the entire day"

I think that approach might only work if both locations are directly north/south from each other, unless I'm thinking about this wrong. If the locations are east/west relative to each other, the shortest shadow won't occur at exactly the same moment.

edit: I guess that would still be a problem if you're using the zenith to determine the time of measurement. The best map I can find of the 2 locations used is [here](https://mathigon.org/step/circles/eratosthenes) and seems to indicate that Alexandria and Swenet/the other location are relatively north/south to each other.

edit 2: some more thoughts. If 2 points at the same latitude but on the opposite sides of the world were chosen, Eratosthenes method wouldn't have worked. The sun would have the same position in the sky at the zenith, but they'd be separated by thousands of miles, implying a flat world. Whether by design or luck, it seems that Eratosthenes experiment only works if the same longitude is used for each location, and otherwise he would have arrived at a very different answer for the circumference of the earth.

Re: How was the size of Earth first measured? (2015)

#63

Post by sgtnoodle »

dylan604 wrote: post #54
bedobi wrote: post #20

I always struggled (and still struggle) with math. A couple of years ago, randomly browsing YouTube, I came across this home made video asking how they figured out the distance to the moon before modern technology. The host starts out small scale showing he can calculate the distance to things in his back yard using trigonometry and then scales it up to the moon. My mind was blown, because no one ever told me that. I…

When I was in school everyone hated word problems, but to me, they were the most clear examples of the answer to "when will I ever use this". Sure, maybe you don't care that a train leaving New York traveling at 55mph while a car leaving Philly traveling at 35mph did any thing, but they were definitely real world examples. I had a physics teacher that had a unique way of providing examples that always revolved around…

I had a calculus professor that asked a physics problem on a quiz, and all the students that understood physics got the problem "wrong". It was something dumb about pulling a wheeled suitcase up an incline at a constant speed, and wanted to know the total torque on the wheels...

Re: How was the size of Earth first measured? (2015)

#65

Post by MilStdJunkie »

The Greeks (or, more precisely, the Eastern Mediterraneans, since a ton of these guys were Phoenician) were jaw-droppingly awesome at this stuff. I wish I could have seen it. It makes you wonder how much knowledge from other places - places with wetter climates, and/or further from the colonial powers of the 19th C - has been lost. One of the contributing reasons heliocentrism disappeared from view was that a large quantity of the Pythagorean and Neo-Pythagorean texts were systematically destroyed. When the texts from Umayyad Spain were translated back in Italy, there were simply very few heliocentric-themed writings among them. It's somewhat remarkable we even got mention of Anaxagoras and Aristarchos.

There's a growing suspicion among some in physics, so far as I can tell from my layman's chair, that many qualities like distance (i.e., the spatial dimensions) could be emergent phenomenon, resulting from a sort of bulk degree of freedom exhibited in macro structures (aka "Space from Hilbert Space"). It's an evocative notion, along with MOND and LQC and suchlike; it sometimes does rather seem like we're looking with the wrong set of eyes, or, rather, assuming things we perhaps shouldn't assume. I wish I had a time machine to, say, 2523, to see how this all resolves. How does it interact with the measurement methods cited in this presentation? Whether the cosmos is far larger than we think, or far smaller, or - perhaps most likely - that the thought of a cosmos being "larger" or "smaller" was an absurd starting point to begin with.

Re: How was the size of Earth first measured? (2015)

#66

Post by willis936 »

crazygringo wrote: post #60
willis936 wrote: post #56

Earlier quoted context omitted.

It doesn't imply it, no. There is an absolute true "first human measurement of Earth's size" and it is not fundamentally unlearnable at this point in history. It's just very difficult to prove and we are far from the due diligence necessary for such an extraordinary statement. It should be properly qualified until we piece together a pretty complete picture of lost civilizations.

Of course it's fundamentally unlearnable. No matter what we do know, we can never prove there wasn't someone else who figured it out even earlier but never wrote it down, or they did but it and all references to it were lost. Most "firsts" carry an implicit asterisk that isn't worth mentioning. The first person to run a 4 minute mile did so in 1954. With the asterisk that somebody else might have already done that mi…

In that case then "earliest known" is the only thing that should ever be said and there is no justification for claiming "first".

Re: How was the size of Earth first measured? (2015)

#67

Post by BurningFrog »

nico wrote: post #42
082349872349872 wrote: post #27

Earlier quoted context omitted.

Wow, TIL the reason Aristarchus' contemporaries didn't accept his heliocentric model...

pages 156-158: “Ironically, when Aristarchus proposed the heliocentric model, his contemporaries dismissed it, on the grounds that they did not observe any parallax effects...” “ so the heliocentric model would have implied that the stars were an absurdly large distance away.” “[Which, of course, they are.]”

Never thought of that. It is/was actually a pretty good argument.

Re: How was the size of Earth first measured? (2015)

#68

Post by ithkuil »

NeoTar wrote: post #17
vermooten wrote: post #13

Earlier quoted context omitted.

Thank you! I've wondered that, can't wait to see what he answer is.

I don't know whether this is true, but I think I've heard it said in connection with this story. Egypt had a solar based-calendar, so (to a decent approximation) on every named date the sun would be in the same place in the sky. So all that would be needed was for it be known that the sun shined straight down the well on (for instance) the 14th day of the 2nd Month of Growth (I had to look up the Egyptian calendar to…

The trickiest part was to know the effective distance component in the North/South direction. Luckily the Nile is roughly oriented that way anyway so the distance between the two cities is roughly the same as the North/South component

Re: How was the size of Earth first measured? (2015)

#69

Post by tgbugs »

bryan0 wrote: post #11

Terrence Tao has an old excellent presentation on the “cosmic ladder” which shows how from this measurement you can build up to measure the largest distances in the visible universe: https://terrytao.files.wordpress.com/2010/10/cosmic-distance...

Ah what a fantastic presentation. It answers a lingering question about the use of spectroscopy and apparent brightness to determine the distance to a star. The key step that I had missed was using the stars with distances measurable by parallax to calibrate the color/apparent brightness so that it could be used for stars that were beyond the distance for parallax. Obvious in hindsight, but wonderfully and clearly explained here.
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