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    Re: watch as compass
    From: Frank Reed CT
    Date: 2007 Jul 29, 04:51 -0700

    Jim, you wrote:
    "You don't even need the local time - just a stick and a piece of
    level ground. Poke a stick in the ground and mark where the end of its
    shadow falls.  Wait.  The shadow will move directly east. "
    
    Yes. For a good portion of the day in most latitudes, the shadow moves
    nearly due east, just as you say. But bear in mind that the path of
    the shadow is not normally a straight line. Most of the time, in most
    latitudes, if you trace the shadow path all through the day, it's a
    hyperbola. The shadow starts out at dawn running towards the azimuth
    where the Sun is rising (that's one asymptote of the hyperbola). Then
    it curves about and, right at noon, the shadow is heading due east
    exactly. During the afternoon, the shadow turns slowly until, in the
    late afternoon, it is running rapidly away from the azimuth where the
    Sun is setting (the other asymptote of the hyperbola). The shadow's
    path along the ground is curved. But I should emphasize here that the
    deviation of the shadow path from straight "due east" is not large
    except close to sunrise and sunset and close to the solstices in
    higher latitudes.
    
    Under the assumption that the Earth is flat (definitely close enough
    for this issue) and under the assumption that the Sun's declination
    doesn't change (also definitely close enough), the path drawn on the
    ground tracing out the end of the shadow of any fixed object during
    the day is a conic section, usually a hyperbola. When the Sun's
    declination is reasonably close to zero (even 10 degrees away is not
    bad), that hyperbola will be close to a straight line running east-
    west. If it's an equinox, then it's exactly a straight line. So, most
    of the time, this rule works just fine. But there are important
    exceptions... If the observer is in a latitude where the Sun does not
    set, the path of the shadow tip is still a conic section. Instead of
    being a hyperbola, it is an ellipse. In short, do not use this trick
    in high latitudes. One interesting special case: if you're in the
    Arctic (northern latitudes, that is) and the Sun just barely sets on
    the northern horizon, then the path traced out on the ground by the
    shadow is a parabola. This is an exceptional case. For most latitudes
    and times of the year, the path of the shadow is a gently curved
    hyperbola, and for most hours of the day, the path is nearly straight
    due east.
    
    I would add that you can use a "spot" of sunlight just as well as a
    shadow to determine compass direction. If you're sitting under a tree
    and you see a nice circular spot of sunlight on the ground beneath the
    canopy of foliage (actually a projected image of the Sun), then it
    will work just as well as a shadow. As long as the air is calm, so the
    spot isn't bouncing around with the wind, it functions just the same
    as the shadow cast by some fixed object. Its path, just like the
    shadow, will be a hyperbola, and during most of the day in most
    latitudes, it will move very nearly due EAST. The error will rarely
    exceed 20 degrees.
    
    And you wrote:
    "Of course, checking your directions this way very often will slow
    your
    progress."
    
    Yep. That's the principal disadvantage of this method and its cousins.
    You have to sit down and observe for at least fifteen minutes. Anyone
    have a quicker method? Something you can do in fifteen seconds instead
    of fifteen minutes? I've been working on a few...
    
    -FER
    
    
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