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    Re: Star - Star Distances
    From: Clive Cooper
    Date: 2010 Apr 27, 02:34 -0700
    I notice you are engaged in a forum regarding Polynesian Navigation: I' m sure you would be aware of Dr David Lewis's studies(?) into this?.  He sailed a steel yacht which from memory was called "Icebird".  He also wrote a book.  Forgive me if you know all that !

    From: George Huxtable <george@hux.me.uk>
    To: NavList@fer3.com
    Sent: Tue, 27 April, 2010 4:20:33 PM
    Subject: [NavList] Re: Star - Star Distances

    Richard Reed wrote, about correcting star-star distances-

    "John Karl's book has some more pairs than Bauer (12 I think, upto 113
    degrees), with a refraction table for each, but no aberration tables."


    A bit of care is needed, for those following that route, if using the first
    printing (2007) of John Karl's book "Celestial Navigation in the GPS age".
    Significant changes were made in that respect in the second printing of
    2009 (which is still labelled as first edition).

    In that first printing, a wrong assumtion was made. Taking an observer at a
    known latitude and a star-pair A and B, it was assumed that if star A had a
    known altitude, then that would also define the altitude of star B at the
    same moment. The problem with that is that there are two distinct times of
    any night when star A has that altitude. These times are equally before and
    after the moment of culmination: when it's rising, somewhere to the East of
    the observer, and when it's falling, somewhere to his West. And, at those
    two times, star B will have two very different altitudes, so the assumption
    in those tables breaks down.

    As I understand it, John's first refraction correction table considered
    (without saying so) only the case when star A would be rising, so it could
    be used only when that star was somewhere to the East, not the West, of the
    observer. Then, it would give the right answers.

    John's later version, in the second printing, handles refraction quite
    differently, and gets around that problem.

    However, that leaves the question of star aberration, which can shift the
    angle between star-pairs significantly, by up to half an arc-minute, or so,
    either way, for the most-distant pairs, depending on the geometry of the
    observation and the time of year. John, in the first printing of his book,
    just accepted the value of aberration at one particular moment in the year
    (New Year), which meant that for some star-pairs the worst-case aberration
    could be doubled. More recently, he has changed this to ignore star
    aberration altogether: a better solution, which limits that worst-case
    error. John accepts, in his explanation, that for high-precision work, it's
    necessary to take another approach which allows for aberration, as Brad and
    Richard seem to be doing.


    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Richard Reed" <richard.reed@idnetfreemail.co.uk>
    To: <NavList@fer3.com>
    Sent: Monday, April 26, 2010 9:53 PM
    Subject: [NavList] Re: Star - Star Distances

    Thanks for all that work!

    John Karl's book has some more pairs than Bauer (12 I think, upto 113
    degrees), with a refraction table for each, but no aberration tables.

    For just one pair so far (I really need a tripod!), I went the long way and
    got aberration-corrected Right Ascension and Declination from Solex 10.2.
    I then used Frank Reed's calculations here:


    Using Frank's distance formula on Regulus-Betelgeuse, 62 deg 26.6' in Karl,
    without refraction, I got 62 deg 26.94' from both the Solex data and the US
    Naval Observatory data.  I then used the Bennett refraction formula as
    modified by George Huxtable and used Frank's refraction distance
    correction.  I was quite happy to be within 0.2 minutes that time, but it's
    only one shot.

    Richard Reed

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