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...
How was the size of Earth first measured? (2015)
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Re: How was the size of Earth first measured? (2015)
#12Reminds me of the Cavendish experiment to measure the Earths mass in 1798 which got to within 1% if the correct value (or the currently accepted value)
Re: How was the size of Earth first measured? (2015)
#13Given the large distance between the cities, how did they communicate to confirm that the sun was indeed overhead at particular time and date?
Thank you! I've wondered that, can't wait to see what he answer is.
Re: How was the size of Earth first measured? (2015)
#14Given the large distance between the cities, how did they communicate to confirm that the sun was indeed overhead at particular time and date?
Well, the time is obviously noon by definition(*), and the date would have been well known as it's entirely predictable. Syene is about a degree or so north of the Tropic of Cancer, so essentially the only date the sun is in the zenith is the summer solstice, and that’s the day they should measure shadow length in Alexandria. Had it been farther to the south, there would have been two such days, still well known and understood by the people of the time, and had been for millennia, and it wouldn’t matter which of the days you’d pick.
(*) This was 2000 years before time zones became a thing and local solar times were disengaged from the wallclock time. Not that ancient Greeks had wallclocks.
Re: How was the size of Earth first measured? (2015)
#15Given the large distance between the cities, how did they communicate to confirm that the sun was indeed overhead at particular time and date?
The key is that this phenomenon was well known and predictable. First get the date right, then wait until local noon for the sun to be at its maximum altitude. The Egyptians had long had excellent calendars, so they could use past records to predict the date.
Re: How was the size of Earth first measured? (2015)
#16> the distance from Alexandria to Syene -- believed to have been about 515 miles Even this part sounds amazing to me. How did they measure distances this long back then?
Land along the Nile was heavily surveyed, yearly, to ensure its course changes were recorded in landownership. > Long distances were measured by professional distance walkers, called bematists, who walked at a very regular pace and counted each step. Shorter distances were measured with lengths of knotted rope by men called harpedonaptai, which means “rope stretchers” https://www.maa.org/press/periodicals/convergence…
Staking claims, where corner posts were placed at half kilometer intervals, were usually paced on foot, estimating for canyons, stream crossings, and other diversions. Some claims were continuous up to 20km by 20 km.
This was in complete wilderness, in the Yukon, British Columbia and so on. Pre GPS. Not that long ago!
They used topographic maps for reference. It is amazing how accurate the claims were, when transferred to modern mapping systems.
Re: How was the size of Earth first measured? (2015)
#17Given the large distance between the cities, how did they communicate to confirm that the sun was indeed overhead at particular time and date?
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 get that date!), and Eratosthenes just needed to measure on that date.
Re: How was the size of Earth first measured? (2015)
#18> He had heard that in the nearby town of Syene midday sunlight shines straight down to the bottom of deep wells
“Nearby” is an interesting descriptor for a town 515 miles away.
Syene was basically the town furthest up the Nile in Egypt. You literally couldn’t get any further from Alexandria and still consider it Egypt.
Re: How was the size of Earth first measured? (2015)
#19[flagged]
Re: How was the size of Earth first measured? (2015)
#20I 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. It was simple, anyone could understand it. When I was in school, all I was told was to memorize abstract formulae like calculating the length of sides of triangles based on angles and known length of one side. It was never contextualized to any actual, let alone interesting or fascinating, applications.