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    Re: longitude around noon (a twist)
    From: Gary LaPook
    Date: 2008 Jun 20, 22:52 -0700

    I found this listing on ebay, any comments?
    On Jun 4, 9:06 am, "George Huxtable" 
    > Frank Reed wrote-
    >  I chatted in my email a bit about longitude around noon
    > | and asked him this:
    > | "Which leads to a question: is there an established name in the
    > literature,
    > | or even in your own jargon, for a fix resulting from a series of ten or
    > | twelve sights taken over a relatively short period of time? I've been
    > | calling it a "rapid-fire fix". Do you know another name?"
    > |
    > | His reply:
    > | "I don't know of a special name.  You're correct, of course, if you can
    > get
    > | a bunch of sights on either side of noon, you can get good enough geometry
    > | to get a 2-D position.  It works with the LOPs, too, in that they provide
    > a
    > | good spread of azimuth around then.  There is a slight catch, however, and
    > | that is, the higher the Sun is in the sky (and therefore the more rapid
    > the
    > | altitude and azimuth change near noon) the more you have to worry about
    > the
    > | curvature of the LOPs.  In some near-degenerate cases (sun within several
    > | degrees of the zenith), the usual straight-line plotting -- or math that
    > | assumes straight-line LOPs -- may not provide the right fix."
    > =================
    > There appears to be some misunderstanding in that dialogue. How does that
    > difficulty arise? I think it is quite illusory.
    > Indeed, the higher the Sun is at noon, the simpler the picture gets, the
    > easier it becomes to determine the moment of noon, and the less is the
    > influence of any North-South velocity. It's because the whole process
    > DEPENDS on that curvature, and the sharper the curvature, the easier it
    > gets.
    > As long as the Sun is within a few degrees of the vertical at noon, you can
    > plot the whole event on a Mercator projection, in plane geometry. The Sun is
    > travelling around a line of latitude at 900 knots or a bit less, the ship is
    > travelling (say) South at 10 knots along a line of longitude, and the zenith
    > distance in minutes is simply the distance between them in miles.
    > Indeed, simplest case of all is if the so-called "degenerate" case where the
    > ship crosses the Equator at the same moment that the Sun, travelling round
    > the equator at 900 knots, passes that same spot. From the ship, it's a
    > zenith noon. Until that moment the ship and the Sun have been approaching at
    > a speed of 900 knots and 10 knots, which combine (quadratically) to 900.06,
    > so the ship speed is having no effect. Sun altitude increases steadily at 15
    > degrees per hour, until that moment. Then, instantly, after they pass, they
    > separate at the same rate, so the altitude falls, again at 15 degrees per
    > hour. The observer's difficult task is to about-face, from East to West, at
    > that moment. But otherwise, determining the moment of noon becomes a doddle.
    > That's because the plot of altitude against time has developed a sharp
    > corner at noon. Its curvature is infinite. And the maximum occurs AT noon,
    > whatever the ship speed was.
    > For noons where the Sun is close to, but not at the vertical, the curve
    > becomes less sharp near the top, and ship speed starts to need correcting
    > for, but these high Suns are just the sort of observation for which Frank's
    > procedure of longitude around noon is, indeed, completely appropriate.
    > Frank continued-
    > | That's a good point about sights very close to the zenith. I had mentioned
    > | previously on the list that there may be a special case when the Sun is
    > | close to the zenith. I still haven't thought through whether it really
    > | screws up the graphical technique or merely requires more stringent rules
    > | for its application.
    > Neither. Quite the reverse, in fact.
    > George.
    > contact George Huxtable at geo...@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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