The Earth Is Not Flat

OCT 25, 2010

A few summers ago I took the picture shown at right of a sunset over Lake Michigan. Unlike the oceans, Lake Michigan has no surf and when there is no wind, the surface can be very smooth as it was on the day I took this photo. Later when I looked at the photo I noticed that the upside-down reflected image of the Sun on the water looked slightly compressed relative to the Sun itself. At first this made no sense to me. Then, in an "Aha!" moment, I realized it is compressed because the Earth is not flat and therefore the surface of Lake Michigan is not flat. Thinking of the surface as slightly curved nicely explains the compression of the reflected image. I sat down and worked out the trigonometry and amazingly I was able to compute the diameter of the Earth just from measurements taken off from this picture and an estimate of how high I was standing above lake level when I took this photo.