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Very thorough explanation, awesome! What I'm more curious of is, how did astronomers measure the radius of the earth and moon several hundred (1000?) years ago?



This set of slides goes over how some astronomical measurements were made hundreds of years ago:

http://terrytao.files.wordpress.com/2010/10/cosmic-distance-...


I had known about some of this before like the eclipses being evidence of a round earth and how the estimate for the size of earth from the well story. From this book: http://www.amazon.com/Theories-Everything-Illustrated-Histor...

What I found most fascinating about the explanations (I was in pre-calc at school at the time) was the math involved. During my classes (or any math class I've ever been in) they gave us formulas and equations but no meaning or real world context. If they'd told us how we could use the distance and angles to figure out what they'd figured out so long ago I think the math would have been much more interesting and brought home the point of why it is relevant to anything.


And that is exactly why I want to collect all the great experiments of history and give them to kids at the right ages to do - to calculate the size of the earth using pencils and shadows and skyline others kids in different countries for their measurements - it's got to stick in the brain better


I think it's a fantastic idea. The most difficult things for me to learn were always those which I don't know how to apply or those which I don't know where they came from. You can't reason over something that seems like magic.


OK - so can we start something?

https://github.com/lifeisstillgood/importantexperiments4kids

I think I can get support for something like this from STEMAmbassadors of the UK. I shall see.

Comments?


Thank you for sharing. This is one of the gems for which I subconsciously mine every day I come to HN.


Wow, that's absolutely brilliant. Thanks for sharing. It's particularly impressive to see how old (and accurate) some of these measurements are.


i got goosebumps - i mean, the people of old are really intelligent! they used whatever piece of data they can scrunge together to piece the truth out.

I feel like these days, we aren't putting in as much effort in these endeavours as the days of old. I wonder why...


The "people of old" were just as intelligent as humans today, they just didn't have the same access to technology or stored knowledge (which is why Wikipedia is so revolutionary in some ways). If you look at the statuary from Classical times or the cathedrals of medieval Europe, you come to realize these people were just like us. Some went through life unthinking, others probably had unrealized gifts, and a few were able to show their talents. Also, I'm no anthropologist, but I believe modern humans have existed longer than wrting and the historical record, so I would conjecture that humans up to 10,000 years ago--perhaps all the way back to the Cro-Magnons of 40Kya--were just as intelligent as people today, just they didn't have the means to express it the way we do.

In some ways, the wasted educations and wasted talent of today is apalling. I was in the Sainte Chapelle in Paris recently and realized no one has created anything like it in 800 years.


That's easy! Rosy retrospection, positivity effect, there are a few biases going on here.


I don't know for the Moon, but for the Earth try this: https://en.wikipedia.org/wiki/Eratosthenes#Eratosthenes.27_m...


The coolest thing about it is that more than 2200 years ago it was already possible to measure Earth's circumference with only 2% error. If not for the dark ages, who knows what world we'd live in now?


The term "Dark Age" to describe the time after the fall of the Western Roman Empire seems, as far as I can tell, to be rather frowned upon by historians. After all, the Eastern Roman Empire continued a lot longer in the form of the Byzantines up to the fall of Constanople in 1453 and, more importantly, there was the rise of Islamic culture - which reach a very high level of civilization during this time.

Having said that, I am personally fascinated by history during this time as it led to the genesis of a lot of our current nation states and the very paucity of the historical record from these times just adds to the romance for me!


Michael S. Malone explores the "dark ages" idea in his new book "The Guardian of All Things:The Epic Story of Human Memory". His conclusion was that it was pretty dark for 5 or 6 centuries after Rome fell - then the "high Middle Ages" began and learning and writing and schools and scholarship were rampant all over Europe and the Middle East. Really opened my eyes on that period.


Islamic civilization took over from Roman civilization from about 632 AD in the Middle East, centered around North Africa, Iraq/Persia, and Turkey at various times over the next 1300 yrs.

Perhaps more important was the Sui/Tang dynasties in China around 600 AD kicking off over 1000 yrs of being the most developed place on Earth. They built the Grand Canal connecting the Yellow and Yangtse rivers, turning them into a single economy based on trading rice for coal.


It's not so much that the "dark ages" intervened in some linear progression of scientific discovery. Rather, it seems to require a precise and finicky set of conditions to get a real scientific & industrial revolution going.

The hard part isn't really the basic scientific discoveries. It's the society-wide political and economic conditions that let capital accumulation go exponential.

The ancient Greeks had working toy steam engines. They could have started the industrial revolution right there. Why didn't they? There are lots of theories. Maybe they hadn't invented good enough ideas about banking and property. Maybe their reliance on slave labor blinded them to the value of mechanization. Maybe their class system kept people with scientific knowledge too far away from people with practical working knowledge.

The bottom line is that scientific knowledge is probably not the limiting factor.


Given the radius of the Earth, they could probably get the radius of the moon by looking at the curvature of the edge of the Earth's shadow upon the moon during a lunar eclipse.


Find the moon's distance by parallax, then the radius follows from the angle it subtends.


For parallax you need to take two measurements at the same time. Given that the distance to the moon is about 384,400 km, a 1,000 km baseline gives an angle of 1/384 radians = 0.15 degree. This requires some a rather sophisticated methods, such as clocks with good precision and a telescope.

The method of Aristarchus is much more clever than that. At 1/2 moon, the earth/moon/sun forms a right angle. The angle moon/earth/sun could be measured as about 3 degrees - something that the ancient Greeks could measure. This gives a ratio of earth-moon/sun-moon distances between 18 and 20.

Then during a lunar eclipse, you can measure the width of the cone of the earth's shadow vs. the moon's width. During a solar eclipse you can see that the moon's angular width is about that of the sun. That information, plus the measured radius of the earth, and a bit of geometry, gives you an estimate of the size of the moon.

http://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_%28A...




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