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    Re: Angular Distance Between Stars By Camera and Sextant
    From: Paul Hirose
    Date: 2012 Sep 24, 16:34 -0700

    Antoine Couëtte wrote:
    > Thank you very much for having indicated that your first published values 
    were computed in the UTC (and not the UT1) Time scale ....
    > Well, Paul, never ever use UTC Time scale with Navigators if not immediately saying so ...
    Navigators "hack" their watches to UTC or a civil time scale locked to 
    UTC. Ideally, that would also be the time scale of the Almanac and sight 
    reduction software. It's not, due to the difficulty of predicting delta 
    T years in advance. Anyway, the present implementation of UTC is close 
    enough to UT1 that the difference can be ignored in ordinary navigation.
    In my program that approximation was not good enough, so I had to ask 
    myself, "if Greg had measured separation angle, azimuth, and altitude at 
    .01' precision, what time scale would he have used?" Surely it would be 
    UTC, so that's the way I wrote the program.
    The source code looks terrible in both my browsers, but, strangely, is 
    quoted almost perfectly in Marcel's message:
    Only the long string in the first statement is malformed. But on someone 
    else's system the path to the file will be different anyway. The source 
    code shows that I'm using UTC, and the UT1-UTC offset.
    Despite the crude user interface, the computation is very accurate. In 
    this example reduction by Patrick Wallace
    my program matches his position at the end of the document within .2 mas 
    (milli arc seconds). Note that one mas is about 3 cm (1.3 inches) on 
    Earth's surface!
    For anyone who has Visual Studio and wishes to duplicate the Wallace 
    example with my little program,
    1. Near the beginning, where he lists all the input values, at "IERS 
    X,Y,DUT1 corrections," my program only has provision for DUT1 (= UT1-UTC).
    2. Remember to change the "accuracy" and "precision" variables in my 
    source code to appropriate values, say, 1e-9 and 1e9 respectively.
    3. To make the program display the separation angle between its 
    computation and Wallace's, force his coordinates into the second star. 
    (I'm assuming the first star represents my program's computation.)
    To do that, immediately after
    // Convert coords from vector to spherical.
    SJ.Spherical sph1Unref = new SJ.Spherical(body1Vec);
    SJ.Spherical sph2Unref = new SJ.Spherical(body2Vec);
    sph2Unref = new SJ.Spherical(
         SJ.Angle.DegreesToRadians(450.0 - 116.44983979538),
    (The "450" converts azimuth to the conventional lambda angle of 
    spherical coordinates.)
    4. The two small methods (functions) at the end of the source code that 
    display angles, can output any of three different formats. It depends on 
    the control string, e.g., +2b°′″ for altitude. The letter controls the 
    units: a = DMS.s, b = DM.m, and c = D.d. The actual number of decimal 
    places is determined by the "resolution" variable I mentioned above. In 
    case you're curious, the + forces a sign to be printed always, and the 2 
    pads the integer degree part with leading space, if necessary, so it's 
    at least 2 characters wide. Thus the digits align with the line below, 
    whether the altitudes are large or small, positive or negative.
    I filter out messages with attachments or HTML.

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