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    Re: Proposed FULL RESULTS AND DISCUSSION Re: Multi-Moon line exercise in 2 parts
    From: UNK
    Date: 2009 Aug 8, 10:53 -0700

    Note te Frank : I have unsucessfully attempeted to register as "amc1753". How 
    should I proceed ?? Thank you for your kind attention and understanding.
    Aug 08, 2009
    Dear Jeremy,
    Please find hereunder full results pertaining to your Moon Observations as I 
    would present them to our community. See preliminary results 05 Aug 
    First, thank you for confirming us the exact meaning of the "ON the Arc" 
    instrument correction, which I had surmised right, as also George Huxtable 
    had the kindness of pointing out directly to me.
    I have used 2 completely different methods to process the data of your example.
    1st Method : LAN (or LAM as you have it :-) )
    Revised results are extremely close from the ones I had posted here 3 days ago, and show as follows:
    Moon Transit south of Moving observer occurs at 09h51m39s7 UT2 (0.1 second apart from previous results)
    Observer's position at that time is : N2149.5E13003.7 (same position) with 
    SDEV equal to 0.5 NM, which yields an observed Latitude accuracy of +/- 1.0 
    NM at 2 sigmas and a Longitude error  of 3.8' at 2 sigmas.
    SDEV defines the dispersion of errors around the "ideal values" in case there 
    would have been no observational error at all.
    The remarks concerning Moon Declination "speed" and Observer's SMG South 
    component being almost equal, both effects even each other out and for this 
    reason (Observer's speed being still slightly greater), UT of Culmination 
    occurs only 2.9 seconds of time after UT of moving observer 's meridian 
    Therefore, positions at requested times will remain unchanged, namely :
    At 09:00 UT (18:00 LT) , DR position was  N2200.8E13006.5 as reckoned from the 
    09h51m39s8 observed Moon fix
    At 10:00 UT (19:00 LT) position was N2147.7E13003.2 DR, same as above
    At 11:00 UT (20:00 LT) position was N2134.5E13000.0 DR, same as above.
    2 nd method : brute force processing of all your 33 LOP's (Marcq Saint Hilaire's Method)
    Method 2A
    For time 09h51m39s7 UT2, with all 33 LOP's I again find exactly the same observed position, i.e. :
    N2149.5E13003.7 with SDEV equal to 0.5 NM (same definition for SDEV). All 
    intercepts fall within +/- .8 NM of running fixes (and therefore no 
    unrealistic/unreasonable single observation)
    Method 2B
    Process the observations 3 at a time, which leaves us with only 11 LOP's to 
    process. At time 09h51m39s7 UT2, I find a very slightly different position :
    N2149.6E13003.7 with SDEV equal to 0.4 NM (same definition for SDEV). All 
    intercepts fall within +/- .7 NM of running fixes with - therefore - no 
    single set of observation out of reasonable range either. In this case, SDEV 
    has slightly decreased down to 0.4 NM vs 0.5 NM, which is very sensible since 
    processing 3 Observations at a time - and treating them as a single 
    observation - necessarily smoothes out some of their individual 
    Note on Method 2 A and B.
    At this step, I would not carry out any deeper statistics (through attempting 
    for example to remove some unknown systematic observation error) because all 
    observations fall within a very  narrow azimuth range (175.1 ? - 183.9?) 
    which would definitely render such results totally meaningless.
    Well, I am impressed by a few facts :
    -	The quality of the horizon as seen from a height of 107 ' (From which ship 
    BTW ? ) Had you had the possibility of observing from a lower altitude, you 
    would have got even better results.
    -	The quality and consistency of all your 33 observations, including the quick 
    turn-around time between some of them (some 30 seconds of time only between 2 
    successive shots, which I personally consider a quite good achievement)
    Additional notes : The quantity of data to process in your example ( some 350 
    numbers to type/enter !!!! when NO single error can be tolerated ) is about 
    the maximum you can realistically process if you do not have automatic data 
    transfer from both your sextant and your Chronometer to your numbers 
    crunching computer.
    This might explain why so few of us have accurately responded to your 
    "challenge", which surprises me (just) a little, but I appreciate that I am 
    quite new to this Wonderful Forum (Attaboy ! Frank)
    As in all cases, longitudes derived from sextant observations can be only as 
    good as your exact knowledge of UT2. If it were 4 seconds of time off, then 
    your longitude will be 1 arc minute off, while your latitude will not have 
    changed by any significant/appreciable amount, event with such a "fast moving 
    declination" Moon. Temptation is sometimes to use GPS time as a value for 
    UT2. This is no longer possible since no leap seconds govern the GPS time 
    which therefore has stayed much more stable than UT/ UT1/2.
    What we now are expecting are your own published results from your GPS 
    observations. I have always thought that GPS is a GREAT opportunity to 
    Celestial Navigation since when you use it as DR position, it immediately 
    calibrates the overall quality of your own observations.
    Best Regards, and Thank you again. Read you soon
    Antoine M. Cou?tte
    Aug 05, 2009
    Dear Jeremy,
    Subject to double checking my computation - which I have not done yet - and 
    working through your example, and assuming that "0.8 arc minute on the arc" 
    means :" from instrument value uncorrected for error, substract 0.8 arc 
    minute to get such value corrected for error ", I would suggest the following 
    results, with TT-UT = 66.0 Seconds of time :
    UT of Moon Culmination as seen from moving observer : 9h51m42,6s
    Diffrence between Culmination and Transit times : 2s8 . The observer has a 
    definite speed towards south ( 13.16 kts south speed component), but - 
    interestingly enough - the moon has a declination decreasing by almost the 
    same value, as its declination goes 12.85 '/hour towards the south. Therefore 
    it explains why both effects almost cancel each other out. This is why both 
    Culmination and Observer's True Meridian transit are so close, by only 2.8 
    seconds of time.
    UT of Moon transit observer's Meridian (i.e. Moon passing due south of moving 
    observer) : GMT 9h51m39s8, or LT = 18h51m39s8
    Position at time of Moon Transit trough crossing observer's meridian :
    N2149.5E13003.7 (sorry I am using Air Navigation Computers notation, since I 
    am an Airline Pilot, which means : 21?49'5 N , and 130?03'7 E )
    SDEV of measures is 0.6 NM, which gives a Latitude error of 1.0 NM with 2 
    sigma and a longitude error of 3'8 with 2 Sigmas.
    At 09:00 UT (18:00 LT) , DR position was  N2200.8E13006.5 as reckoned from the 
    09h51m39s8 observed Moon fix
    At 10:00 UT (19:00 LT) position was N2147.7E13003.2 DR, same as above
    At 11:00 UT (20:00 LT) position was N2134.5E13000.0 DR, same as above.
    LAST POINT : If I have made Instrument corrections the wrong way, then I need 
    to rework your example with instrument corrected values higher by 1'.6 than 
    the one I have used. As a consequence, with the assumption that this 1'.6 
    angle change should/will have no significant effect on both Parallax values 
    and Refraction values as well, then Observed Latitudes will be 1'6 to the 
    south and Observed Longitudes are unchanged by reference to indicated 
    positions hereabove.
    Just be so kind as to confirm me that I have done Instrument error removal in 
    the right direction. I somewhat unfamiliar with the terms "ON the Arc" and 
    "OFF the arc".
    Thanking you for your Kind Attention and Awaiting your reply, I ma remaining,
    Most Sincerely Yours
    Antoine M. Cou?tte
    One last question : With such a Height of eye .... where have you been 
    observing from ? an Aircraft Carrier upper deck ? (e.g; USS John F. Kennedy 
    114 ft !!! )
    [Sent from archive by: antoine.m.couette-AT-club.fr]
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