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    Re: Single-body fix method
    From: Jeremy C
    Date: 2009 Aug 6, 09:47 EDT
    If I may humbly direct you to my "multi-moon" exercise posted only a few hours ago.  This is a post showing two real world examples of using a single body to determine position, both around and away from transit.  Alas, I am not in the air or near the poles; but it is a decent, if time consuming, method of determining position if the navigator knows and accept's the method's limitations and has the time to both shoot and then "reduce" the numbers to derive the position.
     
    Jeremy.
     
    In a message dated 8/6/2009 1:10:11 A.M. Central Asia Standard Time, scheele{at}telkomsa.net writes:

    Can anybody point me to an open-access source dealing with Byrd's and Weems'
    attempts to make use of the "single-body fix method"? I believe Weems
    undertook these tests to aid Byrd in his air navigation in polar regions.

    The "single body fix method" has been the subject of one, perhaps several
    threads on this site, which I have only been paying attention to recently.
    James N. Wilson has also written an article about it which is on the ION CD,
    but I am not familiar with the work as I do not have a professional interest
    in celestial navigation or any of the natural sciences. I understand that
    the method's weakness are the requirement of knowledge of the body's azimuth
    and the limitations it places on the fast-moving observer. I saw a
    digestible  -speaking in very personal terms - description of it complete
    with a derivation of the required formulae in the online ION Newsletter in
    an article about half way down the page by Joe Portney entitled "Portney's
    Corner: The Lost Sub Quick Fix". Here is the adddress:
    http://www.ion.org/newsletter/v11n1.html
    A follow-up reader's letter under the heading "Pondering Portney's
    Ponderables"  in the subsequent online issue claimed/reported on errors that
    appeared in an embedded diagram and in the derivation of the formulae in the
    earlier article. The web address at which this second article can be found
    is:
    http://www.ion.org/newsletter/v11n2.html
    The first article merely alludes to the Byrd and Weems trials involving this
    procedure, involving sights of the sun taken through "the open hatch of a
    seaplane."

    I am still pondering the method. To this end I am reading a chapter in
    Charles Cottter's "The Elements of Navigation" on the subject of "rates of
    change" (of celestial bodies' altitudes), although this particular
    description is limited to meridian observations and is only indirectly
    related to the subject of the "single-body fix method", Cotter's objective
    here being the determination of the sun's maximum altitude. At present I am
    unsure as to why Cotter puts observed changes in altitude of a celestial
    body, a function of the combination of movement of the celestial body and
    the observer's own movement, into a formula that is a "partial integral" (my
    own term), covering the rate of change in one minute of time in one linear
    equation, rather than a "true" integral function, but maybe that's because
    we are talking about a slow-moving observer (on a ship) and it is therefore
    good enough to use an approximation. In any event, I imagine that practical
    application of the method (if, indeed, it is practical at all), where the
    period of observation of a body's rate of change may be a minute or a half a
    minute (for as much as I know), must by necessity involve the "partial",
    rather than the "real" derivative, but I think this is a different
    consideration. To those readers who are familiar with this cited chapter, is
    the method which Cotter explains an approximation as I suspect, or is it
    complete and to be used without reservation as suggested?

    Christian Scheele

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