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    Re: Assumed positions, WAS: IN HONOR OF JEREMY...
    From: Antoine Cou�tte
    Date: 2009 Sep 25, 04:10 -0700

    Dear Peter,
    
    
    
    You are raising a very interesting subject : astronomical fixes without prior 
    knowledge of assumed position.
    
    The "Assumed position" method - actually some kind of "regula falsi" approach 
    . - led to the then revolutionary approach (mid XIX th Century) of the 
    so-called Marc-Saint Hilaire Method, which apparently was pioneered by one 
    (or two ?) different French Astronomer(s?), as we could learn in a most 
    instructive recent thread in Navlist.
    
    When have "Astronomical-fixes-without-prior-knowledge-of-Assumed-position" 
    first ever ever been devised ? I really do not know ... and maybe George or 
    Frank may know better.
    
    
    *******
    
    In France both in the Military Navy and Civilian Merchant Navy (most of the 
    Merchant Navy Instructors come from the Military) , such problem has long 
    been known as Douwes's problem. To the best of my memories, M. Douwe was a 
    Dutch Navigator of the XIX (?) th century who reportedly had already spent a 
    lot of thoughts about tackling this subject. I do not think he did find the 
    exact solution.
    
    The exact mathematical solution for a steady course/speed moving vessel (i.e. 
    immediately obtained from a one shot mathematical computation : no successive 
    computation/approximation loops) has been recently found, not even by a 
    Seaman, but by M. G. HOUNEAU who as I can recall, is a ... (French?) Air 
    Force Colonel who published it there in 1991, see : 
    http://cat.inist.fr/?aModele=afficheN&cpsidt=19474690.
    
    I am not aware that other people might have found this very same solution 
    independently, or at least published it before. But other people did work and 
    publish on this before as you mention it (1981 James van Allen). I would also 
    think that in one of his papers - the third one unfortunately no longer 
    available on the web (who has it, please ??? ) - Dr George Kaplan from the 
    USNO did address this very same subject in depth a little over 10 years ago 
    (see 
    http://www.usno.navy.mil/USNO/astronomical-applications/publications/reports) 
    .
    
    *******
    
    To my sense - and to my burning memories (see the story below) - the reason 
    why so few results have apparently been published before the early 80's is 
    because only by such times has the sufficient computational power been more 
    and more widely available.
    
    By 1980 I had devised on my own 3 independent methods of dealing with this, 
    and I did have to wait until then to successfully run them on my (third type 
    of) calculator. One of these methods had I already "invented" some 6 or 7 
    years earlier when at the French Naval Academy. I had painstakingly but 
    eventually and successfully run only one example then in early 1974 but it 
    had taken me over 10 hours of "manual" computation. I even made a (quite 
    proud) presentation about my method and results to my fellows and instructors 
    who found it ... "interesting indeed, but maybe (or "hopefully" would say the 
    nicest ones in the audience) of some practical interest the future " ... Why 
    such unexpected reaction and feelings ? Simply because WE DID NOT HAVE ANY 
    PRACTICAL COMPUTATIONAL POWER AT HAND THEN !
    
    I doubt whether I was the first and only one to do achieve such result then in 
    1974, but at that time, such methods were TOTALLY UNPRACTICABLE AT SEA ! Such 
    computations can now be carried out (and with no error at all !) in less than 
    once second on a laptop to-day.
    
    *******
    
    Just a quick note : you also mentionned the Earth oblateness/ellipticity and 
    might wonder whether it is difficult to fully take it in account in Celestial 
    Navigation. My view point would be "NOT AT ALL". If you deal with local 
    coordinates - which by chance are one the sets we use in Celnav - and if youy 
    compare with results computed for a fully spherical Earth, the ONLY effects 
    of oblateness are :
    
    - a different parallax value in Height which can be accounted for quite easily 
    at any required accuracy, and
    
    - a parallax in Azimuth. Mathematically speaking, this one can even reach 
    180�, but only in exceptional cases almost totally ruled out by conventional 
    observations. Parallax in Azimuth could be significant only when altitudes 
    are almost equal to 90�, a case when a conventional sextant is almost totally 
    useless, since above 85�-87� heights, swinging around is becoming a quite 
    impracticable maneuver. True, there could be cases with (somewhat) 
    appreciable horizontal parallax, but you can get rid of such (undesirable) 
    effects just trough running one more iteration if required since it will 
    reduce your intercepts lengths. Accordingly any position inaccuracy due to 
    ignoring the parallax in azimuth can then be downgraded to almost any low 
    value you would require : in other words, horizontal parallax effects on an 
    ellipsoid can be minimized to well below one tenth of arc minute on observed 
    coordinates which constitutes the VERY BEST conventional Celnav can EVER 
    achieve.
    
    *******
    
    Best Regards from
    
    
    Antoine M. "Kermit" Couette
    
    
    
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