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    Re: 2-Body Fix -- take three
    From: Peter Hakel
    Date: 2009 Nov 11, 11:28 -0800
    There are two questions that we are dealing with here:

    [1] What is the ship's position?
    [2] Where do the two circular LOPs intersect?

    [1] is the perennial question in navigation.  This is the main question.
    [2] is an abstract mathematical and geometric problem.  This is an auxiliary problem that is solved in order to answer the main question [1].

    [1] has one solution.  [2] has two solutions, one of which is also the solution to [1].
    Additional information (usually DR) is needed to decide which of the two solutions to [2] applies to [1].  Therefore answering [1] with the help of [2] is a two-step process.

    Van Allen's and John Karl's (Gauss?) are methods that solve [2].  This additional information does not enter these methods and is only used afterwards so as to answer [1].

    The intercept method, on the other hand, operates in reverse; the additional information is imported in the beginning with the AP.  Then the (now unique) LOP intersection is found.  In this case we are in fact solving a slightly modified problem [2], let's call it [2a]:
    "Where in the neighborhood of the AP do the two circular LOPs intersect?"

    John is correct that [2] has two unambiguous solutions.  George is correct that there is an ambiguity when solutions of [2] are used to answer [1].  I think that both gentlemen are right, they are just answering two different, albeit related, questions ( [1] and [2] ).


    Peter Hakel


    From: John Karl <jhkarl---.net>
    To: NavList <navlist@fer3.com>
    Sent: Tue, November 10, 2009 7:19:30 PM
    Subject: [NavList 10556] Re: 2-Body Fix -- take three


    George, and others who may be interested --

    Remember we navigators are sensitive to terminology (negative
    longitudes, assumed positions, dip, index mirrors, etc.).  So please
    don't call the two fixes "ambiguous" in the 2-body problem.  The key
    point that everyone needs to agree on is, that, given only the
    altitudes of two bodies and their coordinates, there are TWO
    UNAMBIGUOUS fixes.  Other than outside information, no computer code,
    no reformulation of the equations, can distinguish between these two
    fixes.  Does anyone on the List disagree with that??  If so, tell me
    where I'm going astray.

    And Frank --

    You may have not have found any student confused by the concept of
    assumed position.  But just try asking any CN navigator why we use an
    assumed position in the intercept method, and I'll bet you'll find
    that at least 98% of them respond with a misconception.  Of course, I
    may be wrong; I'm only by going by all the CN books I've read.  Then
    again, as a CN navigator, I may be a bit too sensitive.

    JK




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