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    Re: My first Lunar
    From: Giuseppe Menga
    Date: 2008 Jul 16, 09:48 +0200

    Well, looking at position finding as an optimization problem, where the 
    model is highly non linear and the functional to minimize is not simply 
    quadratic, but shows several local minima, mathematically nothing can be 
    sayd other than, if you starts relatively close to one of these local minima 
    you will find it as solution.
    Usually in these cases, after finding a minimum, you apply a random 
    perturbation to the solution and try again to see if other minima (or a best 
    minimum) exist:
    In this case I assume that all (two) minima have identical functional value 
    so are undistinguishable just from the fitting.
    ----- Original Message ----- 
    Sent: Wednesday, July 16, 2008 6:32 AM
    Subject: [NavList 5858] Re: My first Lunar
    Giuseppe, you wrote:
    "Dear Frank,
    using my clearing algorithm I found:
    time 22:19:38 GMT, pos 14�N 35.3', 61�W 41.3'
    LD 68� 13.13' (sextant LD 68� 19.40')
    The position is roughly 5 miles from yours
    Sounds like a near-perfect match. Incidentally, the "best" GMT would appear
    to be about 22:19:34 according to my calculation, but 0.1' difference in the
    clearing process would correspond to 12 seconds difference in time so I
    don't consider a difference smaller than 6 seconds in time, in any analysis
    of lunars, to be meaningful.
    The "fix" from the two altitudes comes from two altitudes in nearly opposite
    azimuths so that the position is relatively indeterminate along azimuth
    340/160. That is, you can shift the fix five miles or more along that
    direction and there would be little difference in the result. So again, that
    means your result is a near-perfect match with mine, which is re-assuring!
    And this brings up an interesting question. How can this analysis be
    producing different longitudes? Viewing a lunar as a sight for longitude, as
    in traditional, historical lunars, how can there be any ambiguity in the
    final longitude? The few miles difference that we're seeing here might be
    excused but what about the big difference in longitude between the position
    (presumably the correct one) west of Martinique and the other position
    inland in Guyana? The answer, of course, is that the longitude resulting
    from a lunar depends also on the local time. If these sights had been worked
    in the early 19th century, and there was no reliable time kept by a common
    watch, the altitude of Jupiter would probably have been worked to get the
    local apparent time. But that calculation depends on the latitude. So if you
    assume a different latitude, you get a different LAT and when combined with
    the Greenwich Time that comes from clearing the lunar, you would end up with
    a different longitude.
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