4 ms·

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

by CUViper 14y ago

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

rcthompson 14y ago
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.
- abecedarius 14y ago
  Find the moon's distance by parallax, then the radius follows from the angle it subtends.
  - dalke 14y ago
    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_%28Aristarchus%29 http://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_%28A...
stargazer-3 14y ago
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?
- arethuza 14y ago
  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!
  - teeja 14y ago
    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.
  - vorg 14y ago
    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.
- ef4 14y ago
  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.

by CUViper 14y ago

rcthompson 14y ago

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.

abecedarius 14y ago
Find the moon's distance by parallax, then the radius follows from the angle it subtends.
- dalke 14y ago
  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_%28Aristarchus%29 http://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_%28A...

stargazer-3 14y ago

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?

arethuza 14y ago
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!
- teeja 14y ago
  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.
- vorg 14y ago
  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.
ef4 14y ago
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.