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    Re: 3-Star Fix - "Canned Survival Problem"
    From: George Huxtable
    Date: 2008 Jun 11, 14:29 +0100

    I've been looking in a bit more detail at the diagram, provided with Andres
    Ruiz' computation, showing his resultant "cocked hat", and it's left me a
    bit puzzled.
    
    I haven't found a way to print out that plot, so my comments refer only to
    the picture as I see it on my screen.
    
    The final "fix" (affected as it may be by an error in the time of the Pollux
    observation, an error which isn't my present concern) is placed at the
    centre of the plot, at (0.0, 0.0) on the graph, so its actual lat and long
    are not shown on the plot, except as nearby text. But what are the x and y
    scales on that plot?
    
    The y scale is simple enough. It shown changes in latitude, in minutes and
    in nautical miles , which are the same thing, positive going North. If
    angles measured on that plot are to mean anything, then the x axis should be
    to the same scale of miles on the plot, and so a position circle should plot
    as a circle. On my screen, that doesn't happen; a position circle plots as
    an ellipse, horizontally squashed. So on that picture, angles will be
    distorted.
    
    What about the units along the horizontal scale, then? Although there's
    nothing to say so, those are plotted in nautical miles, also, even though
    that scale of miles differs from the miles of Northing. It's only possible
    to quantify shifts in longitude by doing some trig., and arithmetic.
    
    To me, that appears to choose the worst of all possibilities. The two
    scales, horizontal and vertical, should be the same in miles, the vertical
    scale should be MARKED in minutes of lat. (as it is), and the horizontal
    scale should be MARKED in minutes of long., so that lat and long can be read
    straight off it.
    
    ==============
    
    Additionally (and this is a separate matter) Andres' program appears to
    treat all longitudes as Easterly, so that a Westerly longitude is shown as
    negative. To me, this seems somewhat perverse, though I am aware that many
    programs (particularly for astronomy) do so. We navigators work in hour
    angles (GHA and LHA) for our positions of bodies in the sky, and those hour
    angles are always measured Westwards, so that they always increase with
    time. An hour angle is nothing else but the longitude of the body, measured
    Westerly from Greenwich, 0 to 360. Why don't we measure our geographical
    longitudes exactly the same way, so that we simply difference the longitudes
    to get local hour angle? Meeus is an astronomer who sets us a sensible
    example. It seems madness to measure hour-angles as positive Westwards, and
    longitudes as positive Eastwards. Can anyone really justify it?
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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