Circumferemce Of Planet Earth . .

[Evagrius Ponticus]

Hello Friends,

I've been trying for some time to completely understand how Eratosthenes was able to successfully measure the circumference of Planet Earth. I've read his method several times but a complete understanding remains a tad beyond my reach.

In the simplest terms, can anyone explain how he was able to determine what portion of a circle a segement of planet earth represents? Thank You!

http://www.juliantrubin.com/bigten/eratosthenes.html

 

[SydneyGeek]

Let's see...

Sun is directly overhead the Tropic of Cancer (Capricorn in Southern Hemisphere) at local noon on the summer solstice.
That makes the sun's rays go straight through the centre of the Earth, assuming it's a circle.
Next is to measure the angle of the sun where you are, at local noon on the solstice. Subtract from 90, and you get how many degrees you are away from the Tropic. The reason for that is that where parallel lines are cut by another straight line, the angle between the parallel and intersecting lines is the same. At the Tropic, it's 90 degrees. Where you are, it should be 90 degrees less the angle at the centre (of the earth).
Eratosthenes got 7 degrees when he made the measurement. He then calculated the distance between Syene and Alexandria and multiplied it by 360/7 to get the answer.
Does that help?

Denis

 

[MrKowz]

Let's see...

Sun is directly overhead the Tropic of Cancer (Capricorn in Southern Hemisphere) at local noon on the summer solstice.
That makes the sun's rays go straight through the centre of the Earth, assuming it's a circle.
Next is to measure the angle of the sun where you are, at local noon on the solstice. Subtract from 90, and you get how many degrees you are away from the Tropic. The reason for that is that where parallel lines are cut by another straight line, the angle between the parallel and intersecting lines is the same. At the Tropic, it's 90 degrees. Where you are, it should be 90 degrees less the angle at the centre (of the earth).
Eratosthenes got 7 degrees when he made the measurement. He then calculated the distance between Syene and Alexandria and multiplied it by 360/7 to get the answer.
Does that help?

Denis

Did you write that off the top of your head!? Very impressive!

 

[Evagrius Ponticus]

Thanks Sydney - It does help - I will continue to work my way through it. Measuring the angle of the sun is my next challenge

 

[MrKowz]

Thanks Sydney - It does help - I will continue to work my way through it. Measuring the angle of the sun is my next challenge

Don't look directly at it... might sting a bit

I think what you could do is put something with point perfectly vertical on a perfectly level surface. Measure the distance from the base of the apparatus to the top. Then look at the shadow. Measure the distance from the center of the base to the tip of the shadow. You can then use TAN to find the angle.

 

[Atroxell]

Depending on how precise you want to get, you could use a protractor (or something similar) with a tube taped to it's flat side and a plumb line to measure the the sun's angle. When the tube is casting a circular shadow, then you have the correct angle.

That's how we did it in grammar school, once upon a long time ago...

Or borrow someone's sextant--eveyone has one, right?

 

[Norie]

Eh, is the Earth a circle?

Isn't it some sort of ovoid, or geoid, or oddoid?

 

[MrKowz]

Eh, is the Earth a circle?

Isn't it some sort of ovoid, or geoid, or oddoid?

It is. The spinning of the earth causes it to bulge out slightly at the equator due to centrilital force (think about a ball of dough and spinning it). However, for all intensive purposes, we can consider it a sphere.

 

[Norie]

'intensive' purposes?

 

[Taul]

Eh, is the Earth a circle?

Isn't it some sort of ovoid, or geoid, or oddoid?

no no no, only the sky is spheroid, the earth itself is flat, look out of the windows guys.

Whilst on the subject, gravity is a myth, the earth sucks!