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    Shadow stick trivia question
    From: John Huth
    Date: 2009 Oct 15, 19:35 -0400

    Last week I had my class trace out the path taken by the shadow of a gnomon over the course of a day.   The results were surprisingly straight lines.     My initial hunch was that it would be a hyperbola, but since the main goal was to determine east-west (and N+S) with a sun compass, I wasn't so much worried about the rising and setting positions of the shadow-tip.

    So, I thought a bit about it, but hadn't done the actual math of the projection versus latitude and time of year.   We're at 42 degrees North here.   

    My logic was this - at the summer solstice, since the sun rises N of E and sets N of W, you'd get a hyperbola that "points south (meaning the ends of the shadows at morning and evening point south).    Then, during the winter solstice, the hyperbola "points north" since the sun rises S of E and sets S of W.    Good, so far? 

    OK, what about the equinoxes? the sun rises due E and sets due W, but since we're at 42 degrees north, it's still going to be a "south pointing" hyperbola since the stick will have a shadow that's north of an east-west line at meridian passage.

    It would then seem that there is some day, on the "winter side" of the equinoxes where the shadow-stick is close to a straight line for my latitude.   

    Has anyone looked into this phenomenon?   I should not be lazy and perhaps do the math, but perhaps someone in this group has done the math.

    Now, before George H. jumps over me, I realize that the solar declination will indeed change over the course of the day and it will *never* be precisely a straight line, but there's some moment, that, if your froze the solar declination for a day, you'd get a straight line. 

    Thanks in advance for any wisdom!

    John Huth

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