How to Measure the Earth's Circumference

Derivation and brief history of the 1st known measurement of the earth's circumference/radius, devised by Eratosthenes of Cyrene.
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[@physicsalmanac]

Re-oops! The correction to my error at 7:42 also has an error... its should say 39,000 km... not meters.

[@michaeldamolsen]

I really enjoyed this video. The narration is pleasant and well paced, and the editing is great. I wanted to make some small comments about accuracy and such, but I see you have addressed those very well in your Al Biruni video.

[@physicsalmanac]

I’m glad you enjoyed it. Thanks for watching!

[@skivvy3565]

To answer your question about measurement across water: around 600-500bc *Thales of Miletus* was measuring distance of objects by sight and geometry, ie distance of island/ship from shore using his 4th theorem. IV: Two triangles are congruent if two side and an angle are equal. “Thales imagines standing on a beach with water to his right. First he placed a blue marker where he stood. Then he paced an arbitrary distance say 20 paces down shore and placed Red Marker there. Another 20 paces and placed Green Marker. He then imagined drawing a line from the first marker to the ship and extending it. Then he drew a line from red marker to the ship and extended it. Finally he drew a line to Green Marker parallel to the first line. When he was done with that he had two triangles. The triangles are exactly the same size but mirrored (4th theorem). Since one triangle is sitting over Land he could just measure off the length of its side and know that is had the same length as the distance of the object to the shore.” I cannot tell you how painful this is to describe without a simple diagram

[@skivvy3565]

There’s also simple nautical methods for measuring distance to objects on the horizon, and a few more early methods worth looking into that were definitely well known at the time.

[@physicsalmanac]

Thanks for the info! That's a pretty clever method. You're right it's much easier to explain with a drawing... I had to draw it out as I read the procedure so I could understand the method 😆 With the drawing in front of you it's immediately clear.

[@physicsalmanac]

@@skivvy3565 If they knew the distance to the horizon, it's surprising they didn't figure out Al-Biruni's method for measuring the radius of the earth, since the geometry is the same... maybe they had a different way altogether? But how do they do it in open waters? Rhodes to Alexandria is some 560 km or so, while the horizon is only 4 km away.

[@skivvy3565]

@Physics Almanac These are the things that keep me up at night lmao. I’d love to hear if you find any more info yourself, and I’ll check in if I find any interesting anecdotes. Godspeed and good hunting

[@physicsalmanac]

@@skivvy3565 For sure! And if you find something def let me know.

[@marcg1686]

Great video. 👍 Posted it to my Community tab.

[@physicsalmanac]

Thanks Marc!

[@geoffreywilliams9324]

Excellent explanation thanks . .

[@physicsalmanac]

You’re welcome. Thanks for the comment and for watching!

[@profphilbell2075]

How did the measure distance across water? The old rope with knots trick.

[@physicsalmanac]

Thanks for the comment! Could you elaborate? How does the old rope with knots trick work?

[@profphilbell2075]

​@@physicsalmanac Ships used to carry a rope with knots in it at equal distances apart. At the end of the rope was a weight that was designed to cause friction with the water like an anchor does with the sea bed. The point was to determine velocity and use that to calculate displacement. So they throw the anchor out at the stern and let the knotted rope spool out for 30 seconds. Then count how many knots was used. They then have a velocity in terms of knots. This was the derivation of the words knot and nautical. Eventually it was standardised and knots meant the same thing to everyone. The nautical mile simply was the distance in 1 degree of latitude, hence the whole circumference divided into 360 degrees. So 1 degree of latitude is 60 nautical miles which equates to 69.1 miles of normal statute miles.

[@physicsalmanac]

@@profphilbell2075 oh wow, pretty clever. I didn't know that's where we get the term knots. Thanks for the info!

[@alexjohnward]

I think if the boat journey was taken regularly, and the average speed of sail was estimated, and take the average trip times of many trips, you could estimate a very accurate distance.

[@prateekgoyal2650]

To answer your question about measurement across water: posidonius called Jesus to measure the distance as he can walk on water 😂

[@shanent5793]

Didn't Eratothenes use the fact that sunlight reached the bottom of deep wells in Syene or was that someone else?

[@physicsalmanac]

Yes I believe that’s actually how the story goes. That the sun light shines straight down into the bottom of a well in Syene.

[@shanent5793]

@@physicsalmanac it's amazing what can be deduced from some seemingly random fact. Thanks for making these videos!

[@marcg1686]

Yes he did. The Sun will be directly overhead between 23.5°N and 23.5°S (the Tropics) at some time during the year for any observer located in the Tropics.

[@DivergentDroid]

@NathanOakley1980 channel sent me. Nathan reviewed this video today. Thank you sir for your views and opinions!

[@physicsalmanac]

Thanks for stopping by! 🙂

[@marcg1686]

@DivergentDroid. Errand boy.

[@DivergentDroid]

@@marcg1686 An angle is defined as: Two straight lines meeting at a vertex. In geometry a Line Cannot curve! Both by definition and Math, it is impossible to take an elevation angle from the surface of a sphere! See - Rob Durham - A Sextant and a Circle (improved quality). He shows you a cad program will Reject trying to take an angle from the surface of a sphere. Now you are free Mark to believe anything you like but you don't have grounds to tell me I'm wrong when both math and definitions of an angle refute your globe belief. Errand boy - Of course. Nathan tells the truth via facts such as those above. For you to disagree, you would have to change the definition of an angle and how angles work in math. It's not me who is in denial here, it's you.

[@marcg1686]

@@DivergentDroid The fact that I can use the curved roof of my car as an artificial horizon or a puddle of water as an artificial horizon proves your non-understanding of celestial navigation using a sextant.

[@DivergentDroid]

@@marcg1686 Not for the purposes of celestial navigation you can't. The GP has to be in a straight horizontal line to the observer. This means you are on a flat plane. The fact that you don't adjust for dip or height of eye (which are the same thing just two different ways to say it) if on the surface of the sea proves it. If you think you are correct, then why does No CAD program ever made allow you to take the angle from a curved surface? If you think you are right, why don't you petition the dictionary makers to change the definition of an angle? Because it Can't work. You don't understand what makes angle an angle. The adjacent has to be a horizontal plane otherwise, you have no relationship that is the same to establish the angle.

[@photosphotos]

The mean radius is 3959 miles. Using spherical trigonometry that equates to 8” x miles sq if you wanted to understand how to see the curvature however we don’t see that, the horizon is horizontal.

[@jeffreyperez6408]

A mechanichal gear attached to a counter on a boat

[@physicsalmanac]

Are you referring g to how the measured distance at sea? Do you know if the Greeks actually did this? Someone told me the measured knots on a rope being let into the water, and that that’s also the origin of the term knots referring to speed.

[@marcg1686]

​@@physicsalmanacWhat you are referring to is a chip log. The Greeks weren't using chip logs.

[@Birgeyful]

Wallmart did this with a single light source, and found out the floor is curved in all their Wallmarts.

[@physicsalmanac]

See if you can figure out the difference between a light on a walmart ceiling and the sun or a star...

[@Birgeyful]

@@physicsalmanac Neil Degrasse Tyson said the result would be same with small and local sun.

[@physicsalmanac]

@@Birgeyful Well NDT is probably speaking loosely. Its true that if the sun is nearby and the earth is flat, there would also be a change in shadow angle from one place to another. However, how that angle changes would not be the same. So you can differentiate the two by observing how the angle changes with displacement.

[@barryon8706]

@@Birgeyful With a flat earth and a small local sun, the sun would keep going down as you move away from it, but it would be going down more and more slowly. With a globe earth, we see a constant rate of drop as we gain distance.

[@David_Lee379]

@@BirgeyfulSo you concede that Neil DeGrasse Tyson, the same NDT who said “it isn’t f***ing flat” is a credible source. That’s a start.

[@Davii--]

Great video, but all the points that say it was real are questionable and refutable, starting with the existence of this ghost.

[@marcg1686]

Eratosthenes is mentioned in the Suda, a 10th century encyclopedia and Strabo, a Greek historian mentioned him 2000 years ago.

[@photosphotos]

If rays from the sun are parallel, then eclipses do not cause two shadow types. (umbra, penumbra) If rays do come in at all angles, then the Eratosthenes test and the belief that we can test the earth rotundity in the same way are out! Only one of the above can be true and whichever stays means the other “fact” must go... So think about it which one must go?

[@physicsalmanac]

The moon is considerably larger than Eratosthenes stick in the ground. This should resolve your geometric dilemma. Although I suspect you’re not actually interested in the answer.

[@marcg1686]

Eratosthenes wasn't trying to prove the rotundity of the Earth. That we live on a sphere was known beyond reasonable doubt. He was merely trying to calculate R.

[@RB-sz9gv]

Error #3: assuming the Earth is not flat/or the sun is not local invalidates this bullshit experiment

[@marcg1686]

Given that the Sun and Moon are verifyably spherical, it was entirely reasonable to assume that Earth is also spherical.

[@physicsalmanac]

@marcg1686 save you’re breath, my channel got bombarded by flat earthers a while back. There’s nothing you can say that will change their minds. Believe me I tried…

[@RB-sz9gv]

@@physicsalmanac show me a picture of the curve - No CGI

[@RB-sz9gv]

@@marcg1686 an assumption is not scientific evidence. The balls on a pool table or round. Does that make the table round?

[@oxbowspirit4378]

Nathan Oakley 1980 has the answers that you are searching for.👍 Check it out and discover knowledge. 👍

[@barryon8706]

It's worth noting to everybody that Nathan Oakley thinks the earth is flat.

[@David_Lee379]

Nathan Oakley is nothing but a con artist.

[@ThoughtandMemory]

@@barryon8706also he is obnoxious, arrogant, narcissistic and generally an unpleasant person.

[@timetraveler7]

Nathan Oakley is nothing more than a cult leader.

[@marcg1686]

@@barryon8706 He's also a feckless clown. You forgot that.

[@dank4014]

Come discuss this. @NathanOakley1980

[@barryon8706]

Oakley doesn't discuss. He obfuscates, screams, and mutes.

[@dank4014]

​@@barryon8706 I feel he is well spoken, concise, and absolutely will stop the flow of the conversation in order to define exactly what he means if asked >obfuscates care to point out what exactly is "rendered obscure, unclear, or unintelligible" >screams it's a debate, tension gonna happen, get over it. >mutes That is literally a BALD FACE LIE, YOU {EXPLETIVE}. 😄😄

[@David_Lee379]

Nathan Oakley is nothing but a con artist. He is crude, vulgar, and obnoxious. He literally fantasizes about putting his balls in people’s mouths. Oakley NEVER allows anyone to challenge him; he screams over and yes, mutes, anyone who tries. It’s funny how the only time he ever tried to debate a real expert on a neutral platform, he was used to mop the floor with and ran away with his tail between his legs. #gottalietoflerf