Challenge project for the Cape Cod Astronomical Society

Eratosthenes' Experiment

Eratosthenes will always be remembered for the calculation of the Earth's circumference circa 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt). The calculation is based on the assumption that the Earth is spherical and that the Sun is so far away that its rays can be taken as parallel.

Why the Eratosthenes Project?
It didnít really matter what subject we picked. I really wanted to give the members the opportunity to experience the excitement of doing science. Measuring the Earth just seemed outlandish enough that I doubt anyone in the group has tried it before. But doesnít that put many of us at a disadvantage? Only a few members are engineers or scientists. Who knows? It might even be an advantage. Common knowledge is not always right. Most tasks can be accomplished in a number of different ways. In other words, knowing too much can limit our thinking. Donít you have to have a knack for science? Doesnít it require a special kind of thinking?
It requires the same kind of thinking that we all (or most of us) use when deciding how to safely cross a street. We look around, we draw on our knowledge of what vehicles can do, and we make decisions.

People have said, ďI donít know how to get started.Ē What would you suggest?
I can tell you what works for me. The first and most important task is to define exactly what we are trying to do and any constraints the task may have. Would you please give us an example of what you mean?
In this case, the task is to determine the diameter of the earth. The constraints are that we can only use task specific information that was available to people 2200 years ago. For example, they knew that the sky behaved as though the stars were on a sphere rotating relative to the Earth around an axis. They knew this because of the way the map of stars repeated itself through the heavens as the sky and Earth rotated relative to each other. They also knew that the axis of the Earth was on a tilt of 23 degrees relative to the axis of the path of the Sun on that Celestial Sphere. But there is no constraint on devices that we use to measure things as long as those devices do not depend on the diameter of the Earth for their operation. So we cannot use a GPS to do our measurements. But plumb bobs, optical instruments, automobile odometers, magnetic or gyroscopic compasses, etc. are all legal.

You really donít want to tell us how to do this, do you?
That would take away much of the fun. Besides, there are a number of very good ways to approach the problem. What is the best advice would you give to the EP group. Question everything. The way science is taught in schools today, most people think we understand how most things work. We scoff at the things that were misunderstood in the past without realizing that in many ways we still operate out of ignorance. So what do you expect of the EP group What I am hoping for is that the people in the group will brainstorm (i.e. - share thoughts) and work together to get an answer. Getting an accurate answer is nowhere as important as understanding the reasons for any error there might be in the final result of the project and knowing what would be required to eliminate that error. But mostly it will be fun for people to be doing things rather than just reading about them.


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Eratosthenes Project - WSO Method 4 (Werner Schmidt Observatory) (2/21/09)

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