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    Re: , , Re: Time of meridian passage accuracy
    From: Antoine Cou�tte
    Date: 2009 Oct 1, 13:24 -0700

    Dear Gary, Jim and Andres,
    
    
    
    
    As per [NavList 10009] published by Gary, Jim you asked what can be the effect 
    of a quite high Observer's displacement (300 kts full south) as regards the 
    difference in time between LAN and Culmination times. And you submitted a 
    series of 15 shots for our review and interpretation of results.
    
    A bit surprised - not by the high south speed itself - but by the "shape" of 
    the data (heights vs times ) submitted by Jim, I immediately requested 
    confirmation [NavList 10013] that the submitted heights are "Apparent 
    Geocentric for Center of Sun", a inquiry to which Gary most nicely and 
    quickly replied, even in French (Merci Beaucoup Gary !). Yes, "Ho" means - 
    (unless I still get it totally wrong) - "Geocentric apparent center of Sun".
    
    And almost at the same time in [NavList 10014] Andr?s submitted his own 
    results from the data published by Jim in [NavList 10009]. IF I can correctly 
    interpret your results Andr?s's, you observe the following :
    
       - The submitted data perfectly fit to a second degree polynomial curve 
    (mean square error 0.000265  (? ???) , i.e. better than one arc-second ), and
       - The LAN occurs at 17.212754, at a position of N23.299261 and W078.499520 
    (former 3 values are all decimal).
    
    From Andr?s results, it is easy to derive/compute an "observed position" at 
    time 17.000000 (i.e. 0.212754 hour before LAN Time). With a speed of 300 kts 
    towards the south, I get a 17.000000 UT Position at N24.163032 W 078.499520 
    or in usual units : At 17H00m00.0s, the Observer's position is N24?09'8 and 
    W078?30'0
    
    *******
    
    Now, I have a real problem. I cannot reconcile the following facts or results :
    
    - All data presented by Jim to realistically represent the evolution of Ho 
    under the given environment, with in particular a ground speed of 300 kts due 
    South,
    - And the Position results given by Andr?s.
    
    
    *******
    
    Again, the shape of the data supplied by Jim looked stranged to me. So, I did 
    take the time to "reconstruct" the Ho values from Andr?s's results and the 
    environment given by Jim.
    
    Please somebody (Andr?s ? Peter ? Frank ? ) be so kind as to double check all 
    the numbers I am submitting to the community. So, here are the results I got 
    :
    
    Here "Hs" has the exact same meaning as "Ho" in Jim's data
    
    17:00 N24?09'8 W078?30'0 Hs=42?18'1  Z=176.0?  Jim's data : Hs = 42?14'
    17:05 N23?44'8 W078?30'0 Hs=42?46'9  Z=177.6?  Jim's data : Hs = 42?44' 
    17:10 N23?19'8 W078?30'0 Hs=43?13'8  Z=179.1?  Jim's data : Hs = 43?13'
    
    17:15 N22?54'8 W078?30'0 Hs=43?38'9  Z=180.7?  Jim's data : Hs = 43?39' 
    17:20 N22?29'8 W078?30'0 Hs=44?02'1  Z=182.3?  Jim's data : Hs = 44?04'
    17:25 N22?04'8 W078?30'0 Hs=44?23'3  Z=183.9?  Jim's data : Hs = 44?26' 
    
    17:30 N21?39'8 W078?30'0 Hs=44?42'5  Z=185.6?  Jim's data : Hs = 44?47' 
    17:35 N21?14'8 W078?30'0 Hs=44?59'5  Z=187.2?  Jim's data : Hs = 45?06'
    17:40 N20?49'8 W078?30'0 Hs=45?14'5  Z=188.9?  Jim's data : Hs = 45?22'
    
    17:45 N20?24'8 W078?30'0 Hs=45?27'3  Z=190.6?  Jim's data : Hs = 45?36'
    17:50 N19?59'8 W078?30'0 Hs=45?37'9  Z=192.2?  Jim's data : Hs = 45?49'
    17:55 N19?34'8 W078?30'0 Hs=45?46'3  Z=193.9?  Jim's data : Hs = 45?59'
    
    18:00 N19?09'8 W078?30'0 Hs=45?52'4  Z=195.6?  Jim's data : Hs = 46?06'
    18:05 N18?44'8 W078?30'0 Hs=45?56'2  Z=197.3?  Jim's data : Hs = 46?12'
    18:10 N18?19'8 W078?30'0 Hs=45?57'8  Z=199.0?  Jim's data : Hs = 46?15'
    
    18:15 N17?54'8 W078?30'0 Hs=45?57'1  Z=200.7?  Jim's data : Hs = 46?16' 
    18:20 N17?29'8 W078?30'0 Hs=45?54'1  Z=202.4?  Jim's data : Hs = 46?14'
    18:25 N17?04'8 W078?30'0 Hs=45?48'8  Z=204.1?  Jim's data : Hs = 46?10'
    
    18:30 N16?39'8 W078?30'0 Hs=45?41'3  Z=205.7?  Jim's data : Hs = 46?04' 
    18:35 N16?14'8 W078?30'0 Hs=45?31'5  Z=207.4?  Jim's data : Hs = 45?56'
    18:40 N15?49'8 W078?30'0 Hs=45?19'5  Z=209.0?  Jim's data : Hs = 45?45'
    
    18:45 N15?24'8 W078?30'0 Hs=45?05'3  Z=210.6?  Jim's data : Hs = 45?33'
    18:50 N14?59'8 W078?30'0 Hs=44?49'0  Z=212.2?  Jim's data : Hs = 45?18'
    18:55 N14?34'8 W078?30'0 Hs=44?30'6  Z=213.7?  Jim's data : Hs = 45?01'
    
    19:00 N14?09'8 W078?30'0 Hs=44?10'1  Z=215.2?  Jim's data : Hs = 44?41'
    
    IF, and IF again, my assumptions here-above are right, and IF my results are 
    right - this is why it is so important that they can be independently 
    crosschecked - we can see that the data I am computing differ very 
    significantly from the data supplied by Jim.
    
    In all cases, I would be extremely surprised that, given this very special 
    environment, observed values can be exactly fitted to a simple 2nd degree 
    parabola.
    
    So I would raise the following question ? Do the data provided by Jim 
    realistically represent what I understand they should represent in their 
    explained environment ?
    
    If so, would you please Jim provide the exact position and time you have used 
    to derive all these data. Once you just give one position and its time tag, 
    it is extremely easy to derive all the others. I would certainly be very glad 
    to discover that there exists one "real case" where the time vs heights data 
    perfectly fit to a parabola over such a wide times and heights span,
    
    If the data do not realistically represent "true world", then what can we 
    realistically deduce from them ?
    
    And ... if I am totally "off track", please excuse me - because among other 
    reasons I am wasting your time - , and be so kind as to show me the right 
    directions.
    
    
    Thank you for your Kind Attention, for your Time, and Best Regards
    
    
    Antoine
    
    
    Antoine M. "Kermit" Couette
    
    
    
    
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