Easier Method to Calculate Earth's Circumference

[marcusau]

My professor was showing us how to calculate the Circumference of the Earth using Eratosthenes method, as shown here. I completely understand this method. http://www.bsin.k12.nm.us/Curriculum/CAP/completed%20files/astronomy/completed%20files/eratosthenescircumf.html

However he told us he had an easier method and to use it. I'm not sure if it works, however. I have attached the slide from his lecture that explains what he was saying to do. I understand Eratosthene's method because the sun's rays are directly over the southern most stick and the shadow cast by the northern stick then can be used to find the angle that subtends the arc, which is the distance between the two sticks.

I suppose using his method you have to measure the angle cast by both sticks using a protractor, rather than having the option to use geometry like in the original.

Also, I am not sure about the direction of the shadow cast by the sun based on the way he has the sticks are oriented, given the cardinal directions given in the diagram.

Thanks for any help or input.

 

[Simon Bridge]

The diagram looks like the same method, just that the Sun need not be directly overhead as in your description and the one in your link. It is the difference between the two shadows that counts - if you wait for one of the shadows to have no length, then the math is probably easier.

 

[Huyen401]

Hi there,

I can definitely see why you are confused about your professor's method. It seems like there are a few things that are not quite clear.

First of all, I think you are right that your professor's method requires measuring the angles with a protractor instead of using geometry like in Eratosthenes' method. This might make it a bit more challenging to get an accurate measurement.

As for the direction of the shadows, I'm not sure either. It's hard to tell from the diagram which way the sticks are facing and where the sun is. Maybe it would be helpful to ask your professor for clarification on this point.

In any case, I think it's great that you have a good understanding of Eratosthenes' method. That one has been tried and tested for centuries and is considered pretty accurate. I'm not sure about your professor's method, but it might be worth exploring and comparing the results to see how they compare.

Good luck with your studies!