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    Re: Multi-Moon line exercise in 2 parts
    From: George Huxtable
    Date: 2009 Aug 11, 00:36 +0100

    Peter Hakel wrote
    
    "So this "rapid-fire" procedure could be a viable backup if indeed only one
    celestial body is observable (like during the day) and you want a fix "now"
    rather than performing a running fix a few hours later. "
    
    Jeremy's observations were of the Moon. If the Moon is observed in the
    daytime, it can usually be crossed with the Sun. If at night, it can be
    crossed with a star. Either will provide what the navigator seeks; precision
    without an immense load of work in achieving it.
    
    He asked- "In the absence of a practical method of measuring the body's
    azimuth to sufficient accuracy, what else can one really do?"
    
    Simply wait. Until there's a decent change in azimuth. That's the
    time-honoured method of doing celestial navigation: the complete opposite of
    this "rapid-fire" method. Attempts to compress the time-span by taking so
    many observations, and discarding precision, are counter-productive. You can
    do far better by taking just two observations, either well-separated in
    time, or of separate objects. Better, though, would be three, to provide a
    cocked hat. Not thirty-three!
    
    Peter postulates special circumstances- "if indeed only one celestial body
    is observable (like during the day) and you want a fix "now" rather than
    performing a running fix a few hours later. " . Yes, then the method will
    give a result, providing impared accuracy for enhanced workload, if that's
    necessary and adequate, and no alternative exists. As long as the procedure
    is presented in that light, fair enough. But not if it's put forward as
    "this is the way to navigate".
    
      Peter continued- "Another method quoted here recently (post #9376)
    involved measuring dh/dt, the rate of change of a body of known azimuth -
    say by timing the rising or setting of the Sun disk at equinox.  It is
    possible that there is some fundamental connection between that method and
    the rapid-fire procedure, since the latter also inherently includes dh/dt
    information.  The rapid-fire procedure is certainly more available for
    practical use, since you don't need to know the azimuth and you can do it at
    any time provided that the sky is clear enough."
    
    Yes. A single altitude puts you somewhere on a circle around the GP of the
    body observed. At different positions around that circle, the rate of rise
    (or fall) differs, in the range zero to some maximum, which is never greater
    than 15 degrees per hour. In principle, if you could measure that rate with
    sufficient accuracy, it could tell you where you were on that circle. In
    normal altitude navigation, altitudes are measured, routinely, to within 1
    part in 5000 of the maximum range of 0 to 90 degrees. To do similarly well
    by using rate-of-rise, you would have to measure that to within 1 part in
    5000 also. To do that by timing the rising or setting of the Sun, which can
    be over in 2 minutes, would call for timing that to a fortieth of a second
    of time, and for establishing contact of the Sun's limbs with the sea
    horizon to within a third of a second of arc. It's completely impractical,
    just as establishing position around that circle by a measurement of azimuth
    is completely impractical. Only at sea, mind you. On land, measurement of
    azimuth can be highly precise.
    
    Jeremy has provided the list with useful real information by which we can
    assess the drawbacks of the proposed "rapid-fire" method. From his comments,
    he takes a realistic view of its limitations. So should we all.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
    
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