Yesterday we were near Naples, Florida on a rather cool day. We had just had lunch on the beach. My daughter got up, somewhat frustrated by the fact that she could not tan and lie motionless without shivering. My polar bear son had just come back to his towel from his third dip in the gulf, when I noticed that my shadow was longer than I had expected. Using my sandals as a unit of measure, I recorded the length of my shadow. When we got back to our rented home, using the 18” tiles in the living room, I converted the seven-lengthwise and one sideways- sandal lengths into a shadow length of 7.75’. I told my daughter you could still tan: tan-1(6.17/7.75) = 38.5 o. This was the angle made between the sun and the horizon on Dec 28th in Naples, Florida. That means that it forms about a 90 - 38.5 = 51.5 o angle with the zenith. At 12:00 PM on Dec 21, the sun was at the zenith at a latitude of 23.5osouth. On average there is an apparent movement of 23.5 o per 365.25 days/4 =0.257 o/day because in one season the sun will be overhead at the equator and not at the Tropic of Capricorn. Between Dec 21 and the 28th this spells out a total movement of 7 days*0.257 o/day = 1.8 o. 51.5 – 23.5 – 1.8 = 26.2 o N is the predicted latitude for Naples according to these measurements. Actual latitude of Naples : 26.141 oN. Today was a much warmer day and our family and I had a lot more fun. But if it had not been so cool yesterday, I would not have turned the length of a shadow into such a neat calculation of Naples’ latitude.
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