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Re: Eratosthenes and plumb bobs

To some extent the discussion on this thread concerning details of longitude and latitude, assumptions on map construction, etc., have missed the mark, IMHO. The real value of the kind of project Ken Murray asked about is to help students grasp the fact that we really do live in a round world, not flat like some would argue, and that they can make observations which will prove it.
We had a speaker on our campus a few years ago, I am embarrassed to admit, who was the president of the Flat Earth Society. (He died recently, by the way. His name was Charles Johnson.) He was invited to campus by the science student senator as the main speaker for science emphasis week. Needless to say, the faculty were not happy. But, that said, I must add that this experience has provided endless opportunity for those of us who teach gen ed physics, astronomy, and I suppose other subjects, to discuss the importance of knowing some basic facts about the world they live in and how easy it is to prove, or verify, some of those basic facts, so you're not persuaded by bogus arguments like those of the Flat Earth Society. (Or the recent FOX 'moon landing hoax' TV show !)
One of the most important of those basic facts has to be the shape of the world we live on. I applaud Ken and high school teachers like him who stimulate their students in this way, so they want to check things out for themselves.
Let me describe two experiences I have had that prove that we live on a round, not flat, surface. The first was printed in The Physics Teacher a number of years ago. (TPT Nov. 1987, p 500) It happened on an airplane where I and a colleague were flying from Chicago to Atlanta, along a line which was almost due south. As we were taking off the sun was setting. Then, as we gained altitude, we saw the sun come back up and then set again. On my wristwatch I noted the times, and found the two sunsets were about 17 minutes apart. Getting the cruising altitude from the captain after we landed, and doing a little geometry, we were able to estimate the radius of the earth. Of course the fact of seeing two sunsets from different altitudes is the proof that the sun was setting over a curved horizon. Finding the radius of that curvature is just detail.
The second experience happened a few weeks ago. I happened to be in Tucson, AZ, and one evening was looking at the stars, finding what was familiar. I found Polaris, the pole star, and using the only angle measuring instrument at hand, my hand, I estimated the angle from the north point on the horizon up to Polaris to be a little over 1-1/2 hand spans. (The hand span at arms length is about 20 degrees for most people. Mine is just slightly over that.) When I got back to my home in Roy, Utah (near Ogden) the next night, I did the experiment again and found that Polaris was just over two hand spans above the horizon. The difference in latitude between Tucson, AZ, and Roy, UT, was thus a little under 10 degrees, by my crude measurement. Now, such an observation proves that the earth is round. To estimate the circumerence, the details, I had to get the north-south distance between the two cities from an atlas (and yields something over 20,000 miles, not bad for such a crude measurement). But, the fact of different elevation angles for Polaris between those two cities proves that we live on a curved planet. The experiment could be done better, with more precision, if I had taken along a protractor or made more careful measurements of the angles, but the effect was clear enough with simple hand measurements.
I would encourage Ken and his students to continue this kind of exploration and testing. It is important also that they become astute observers of the world around them. You never know when you will stumble onto something of significance.
Now, if I could only meet the Flat Earth Society president again, and ask his explanation of my observations. Oh, well.

Rondo Jeffery
Weber State University
Ogden, UT 84408-2508