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    Re: shadow stick trivia question
    From: Frank Reed
    Date: 2009 Oct 15, 17:38 -0700

    Ignoring changing declination, the source of light (the Sun!) traces out a 
    circle in the sky. It's a small circle, as opposed to a great circle, unless 
    the declination is zero (at the equinoxes for the Sun). Now the end of your 
    stick is a fixed point. If you connect the points on the small circle in the 
    sky with that point and then project through to the shadow of the end of the 
    stick, you get a cone. And what shapes does a cone make when it intersects a 
    plane surface? The shadow of the end of the stick will trace out various 
    conic sections. In most latitudes, you will get hyperbolas, except at the 
    equinoxes when you get a straight line. At some latitudes, you will get 
    circles, ellipses, and somewhere there's a parabola...
    PS: while changing declination will change things slightly, it's probably 
    worth mentioning the refraction also slightly distorts the traced shadow 
    paths, flattening the cones where they are near the horizon. Far more 
    important than these factors is the fact that the surface of the Earth is 
    rarely close to being a true plane.
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