How was the size of Earth first measured? (2015) • Hacker News Board

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

#91

Post by anvandare » Sun, Aug 27, 2023, 4:29 AM UTC

demondemidi wrote: post #86

How did Eratosthenese synchronize the measurements? That seems like the biggest challenge: sync'ing two clocks and transporting one to a place 500 miles away without losing time? 2000 years ago?

The summer solstice ("the longest day of the year") is always the same date regardless of your latitude: June 20th/21st (in the northern hemisphere).

And assuming Syene is on the same longitude as Alexandria[0], Syene's noon is Alexandria's noon.

  Alexandria:       31°11′51″N    29°53′33″E
  Syene:            24°05′20″N    32°53′59″E
  Tropic of Cancer: 23°26′10.4″ N

[0] It isn't, which contributed to the measurement error, but close enough is good enough.

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

#92

Post by ck2 » Sun, Aug 27, 2023, 4:33 AM UTC

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...

The way a few very very smart ancients figured out how things actually are in the solar system with just trivial observations and feeble measurements makes me realize that is exactly what modern astronomers are doing with the universe.

Thousands of years from now someone will do a presentation on how a few of us "ancients" correctly estimated the distance to other solar systems with such poor instruments and how their modern measurements from actually going there show we were only 10% off!

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

#93

Post by defrost » Sun, Aug 27, 2023, 5:03 AM UTC

labster wrote: post #80

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...

The thing that stood out to me was the second rung of the ladder, the Moon. Having a large companion satellite is not a prerequisite for life (probably), so how would aliens without one bridge this gap? It seems like it would take a lot more physical theory beyond simple geometry to get there.

If you can find a copy I can recommend The Tragedy of the Moon which covers such questions (from a 1973 perspective), also raising the advantages to land based life moving from the oceans with the assistance (or forcing) of the tides and tidal zones.

As a sub thread bonus I've got a sneaking suspicion Terence Tao read this collection of essays about the same time he met Paul Erdős in Australia in the early 1980s.

https://en.wikipedia.org/wiki/The_Tragedy_of_the_Moon

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

#94

Post by willis936 » Sun, Aug 27, 2023, 5:10 AM UTC

andrewprock wrote: post #78

willis936 wrote: post #25

"First" is awfully confident assertion about an event thousands of years ago. "Earliest known" is more accurate.

If you study the context and development of Greek culture, astronomy, and mathematics, a good case can be made that if it wasn't Eratosthenes, it was another Greek astronomer.

Babylonians got pretty far from what we can tell. We don't really know how far.

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

#95

Post by drpixie » Sun, Aug 27, 2023, 5:29 AM UTC

alehlopeh wrote: post #79

drpixie wrote: post #74

Earlier quoted context omitted.

Unless the sun was VERY close, the actual distance doesn't matter. What matters is that the sun (or a star, or whatever you use as a reference) is so far away that there is no practical difference between "far away" and "even further". For practical purposes, we treat the sun as being an infinite distance away, and the error caused by it being ONLY 93,000,000 miles away is much smaller than Eratosthenes could measure…

Good answer but weirdly judgy last sentence. More like, a handful of ancient Greeks had a better understanding of geometry than most of us, just like a handful of us has a better understanding of geometry than most of us. And of course, a handful of us has a better understanding of geometry than most ancient Greeks.

Didn't mean to come across judgy :(

Apparently the ancient Greeks didn't have much, if anything, in the way of symbolic algebra or calculus - what we mostly think of as "maths".

Instead their normal tool for mathematical logic was geometry. An educated Greek would have used geometry much like we use algebra.

For most of us, given a non-maths problem (eg physics, chemistry, almost anything in real life...) the first thing we do is express it as an algebra problem, and solve that. The ancient Greeks used geometry in a similar way.

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

#96

Post by jaggederest » Sun, Aug 27, 2023, 5:43 AM UTC

labster wrote: post #80

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...

The thing that stood out to me was the second rung of the ladder, the Moon. Having a large companion satellite is not a prerequisite for life (probably), so how would aliens without one bridge this gap? It seems like it would take a lot more physical theory beyond simple geometry to get there.

> Having a large companion satellite is not a prerequisite for life (probably)

I don't know, there's a sibling comment to this one that brings up some proposed benefits to having a moon.

It's possible that the foundation of life itself relied on having tidal variation of some kind, since AFAIK the equivalent of early amino acids were formed in tidal pools cut off from the main ocean and cooked under the stress of UV and evaporation.

Obviously not something we'll know for sure until/unless we find other organic life, but it's interesting to think about something like having a large orbital influence being a requirement.

Plug that into the fermi equation with observed planets with a moon >0.2% the size of the parent body and it has a definite damping effect on the probability of observing complex life.

Edit: Also shocked I had to revise my numbers, the moon is only 1.2% of the weight of the earth. I thought it was something more like 10% - so you can probably put "tides too strong to allow life" under the other side of that fermi equation factor as well!

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

#97

Post by whatshisface » Sun, Aug 27, 2023, 6:00 AM UTC

oxygen_crisis wrote: post #75

divbzero wrote: post #59

5% error is incredible. I wonder what Eratosthenes thought of his own measurement. Did he believe it was accurate? Or questioned if unknown factors could have thrown off his calculation?

He measured it in "stadia" and there was no consensus about exactly how long a stadion was. The definitions ranged widely, from ~150m to ~210m. The low error assessment comes from magnanimously (but baselessly) choosing to use the definition of a stadion which assigns Eratosthenes the lowest error. https://en.wikipedia.org/wiki/Stadion_(unit)

>An empirical determination of the length of the stadion was made by Lev Vasilevich Firsov, who compared 81 distances given by Eratosthenes and Strabo with the straight-line distances measured by modern methods, and averaged the results. He obtained a result of about 157.7 metres

Sounds like there are other lengths given by Eratosthenes which could be used to tell what he meant by one stadion.

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

#98

Post by unwise-exe » Sun, Aug 27, 2023, 6:03 AM UTC

Hayvok wrote: post #71

nico wrote: post #42

Earlier quoted context omitted.

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.]”

I’m not familiar with the Ancient Greek objections here, but I remember Renaissance scientists being hung up on this same thing. They had measured the visible diameter of stars and without any parallax, would’ve also meant that the stars were absurdly large in addition to far away. I don’t think they had a problem with the distance, per se, but the implied size. (You have to treat stars as points - any perceived diam…

Yeah, using basic geometry to calculate the size of a star from it's distance and the size of the dot it makes in your telescope, doesn't give sensible answers when the size of the dot is due to quantum diffraction (an Airy disc). And since that's named after a guy who lived in the 1800's, you can guess how much the ancients knew about it.

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

#99

Post by whatshisface » Sun, Aug 27, 2023, 6:03 AM UTC

jan_Sate wrote: post #82

This estimation method would only work under the assumption that earth is a spherical. Now that we do know that it's a sphere. But how could you figure that out back in 2000 years ago?

We know from Aristotle that they had some sense of how everything falling down would tend to produce a sphere, if "down" was perchance a point.

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

#100

Post by DiogenesKynikos » Sun, Aug 27, 2023, 6:23 AM UTC

StackOverlord wrote: post #43

nico wrote: post #42

Earlier quoted context omitted.

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.]”

http://homework.uoregon.edu/pub/emj/121/lectures/tycho121.ht... > Tycho Brahe (1546-1601) proposed an experiment that would determine whether or not the earth goes around the sun. Basically, if the Earth orbits the sun, nearby stars should periodically "move" back and forth in their position with respect to more distant stars every 6 months. If the Earth was stationary (at the center of the Universe, this wouldn't oc…

Yes, but historically, scientists ended up accepting the heliocentric model long before the first stellar parallax was measured.

The heliocentric model's parsimony (explaining many different phenomena, such as retrograde motion of the inner planets, with the fewest assumptions) and various supporting observations (such as Venus' phases, which rule out any strictly geocentric model), combined with a physical theory that grounded the model (Newton's laws) rendered any alternative implausible by the late 1600s at the latest. It would be nearly 200 years before parallax was first detected.