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Analemmas

  The puzzle here is to figure out how this photograph was made (assuming that it was not custom-made in a paint program, like I thought at first):

  Pretty strange, but entirely real (well, except for the streaks coming down from the sides and the middle of the figure-8; I don't know how these were made, but they were probably not made through the same process).  I found a description of this effect at http://www.analemma.com/Pages/framesPage.html; here is what I learned there:


  There are two factors to consider when noting this effect.  First, the earth's orbit around the sun is not a circle, but an ellipse; second, the earth rotates in a plane that is at an angle to its orbital plane.

  The elliptical orbit means that the earth is closer to the sun at some points in its orbit than it is in others. When it is closest, the rotation of the earth in 24 hours is not enough to return to facing the sun, as the earth moves past the sun more quickly.  Or, more accurately, the earth moves past the sun just as quickly, but it is closer to the sun, so the angle between the two changes more with the same amount of distance.  The reverse happens when the earth is on the far edge of its orbit; it is farther away from the sun, so moving a given distance causes a smaller angle change.


Diagram from http://www.analemma.com/Pages/framesPage.html

  The elliptical orbit accounts for the east-west movement of the sun at a given time of day; the earth's tilt accounts for the north-south movement.  In the summer in the northern hemisphere, the earth is tilted so that the sun is in the middle of the sky, but in the winter, it is nearer to the southern horizon. We have already discussed this in class; here is a diagram that may or may not help clarify this (the dots orbiting the Earth are representative of the location of the sun in the sky at different times of year):


Diagram from http://www.analemma.com/Pages/framesPage.html

  The sum of these two effects, the annual east-west shift and the annual north-south shift, leads to an effect called an 'analemma', which leads to the visual effect of the sun appearing, at the same time each day, to move like this:


Diagram from http://www.analemma.com/Pages/framesPage.html

  Or like this:


  So this picture was probably taken by having a camera take a picture from the same location, at the same time as determined by an accurate clock (not the sun; that's the whole point!), roughly once a week for the duration of a year.  That simple, yet that wierd.