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    Re: Time of meridian passage accuracy
    From: Gary LaPook
    Date: 2009 Oct 02, 02:00 -0700

    Here is the rest of the data.

    The longitude for all data is 79º  26.5' West

    Meridian passage occurred at 17:16:32 Z at which time the Ho was 43º 46.9' and the latitude was 22º 47.0' North.

    Time             Ho                         Latitude                    Azimuth

    17:00:00     42º 14.1'                  24
    º   09.7'                    174.9º
        :05         42º  44.2'                  23   44.7                     176.4
        :10         43º  12.6'                  23   19.7                     177.9
        :15         43º  39.1'                  22   54.7                     179.5

    17:16:32    43
    º  46.9'                   22º 47.0'                     180.0º      Noon

        :20         44º  03.7'                  22   29.7                      181.1
        :25         44º  26.4'                  22   04.7                      182.7
        :30         44º  47.1'                  21   39.7                     184.4
        :35         45º  05.7'                  21   14.7                     186.0
        :40         45º  22.2'                  20   49.7                     187.7
        :45         45º  36.5'                  20   24.7                     189.3
        :50         45º  48.7'                  19   59.7                     191.0
        :55         45º  58.6'                  19   34.7                     192.7

    18:00:00    46º  06.3'                  19   09.7                     194.4
        :05         46º  11.7'                  18   44.7                     196.1
        :10         46º  14.8'                  18   19.7                     197.9
        :15         46º  15.7'                  17   54.7                     199.6
        :20         46º  14.2'                  17   29.7                     201.3
        :25         46º  10.4'                  17   04.7                     202.9
        :30         46º  04.4'                  16   39.7                     204.6
        :35         45º  56.0'                  16   14.7                     206.3
        :40         45º  45.5'                  15   49.7                     207.9
        :45         45º  32.7'                  15   24.7                     209.5
        :50         45º  17.7'                  14   59.7                     211.1
        :55         45º  00.6'                  14   34.7                     212.7

    19:00:00    44º  41.4'                  14   09.7                     214.3

    I created this data set by choosing the time of meridian passage and choosing the latitude at noon. I then adjusted the latitudes at the rate of 300 knots or 25' of latitude for each five minute period. I then went to the navy navigation website at:


    and found the GHA of the sun for the chosen time of meridian passage and used that for the assumed longitudes. Then using the adjusted latitudes for each of the observation times and the longitude at noon I used the navy website to calculate the computed altitudes, Hc,  and azimuths. I then called the computed altitudes the observed altitudes,  Ho.

    Notice that the difference between meridian passage and maximum altitude is almost an hour. If you look at H.O. 249 or H.O. 214 and run your finger down the columns you will see that the altitude will not start to get lower until the rate of change of altitude exceeds the rate of latitude change at 300 knots which is 20' per one degree change of LHA. Looking at latitude 18
    º declination 23º contrary name you will find this happens at LHA 16º, an hour after meridian passage.


    antoine.m.couette@club-internet.fr wrote:
    Dear Frank,
    In reply to your post in [NavList 10031], I am very sorry that in [NavList 10014] I have messed up with your files arrangement and title logics. I thought that with the site architecture it would be helpful to other readers to title-specify which post(s) I was replying to.
    Promised ! I won't do it again.
    Therefore you may as editor remove [NavList 10014] since I have observed that from time to time apparently some files might have been removed. Please accept my most sincere my apologies.
    And I am submitting again here-under my query which was first stated in [NavList 10014].
    Dear Gary, Jim and Andres,
    First of all, and since the Data first published in [NavList 10009] have been computed/derived and published by Gary and not by Jim, I earlier misinterpreted this and I am sorry for this misunderstanding. Apologies to both of you Jim and Gary.
    I again regret that the "unclear/messy" appearance of my post [NavList 10014] might has concealed the MAIN POINT I have adressed and which I am summarizing here-under with new words. Sorry for the "strict" presentation with (1) , (2) , ... but I hope it helps grasping the subject better and thus helps readers' attention.
    (1) - First in [NavList 10009] Gary submitted data to the Community and requested from us some feedback on these data, essentially as regards the difference between LAN and Culmination times in his example.
    (2) - Andres subsequently analysed Gary's data [NavList 10014] and - from his statement "mean square error 0.000265" which I interpret as being 0.000265 Degree - he seems to find that these data derived by Gary almost EXACTLY match a second degree parabola.
    (3) - From my own interpretation of Andres's results, - is it correct ? Please Andres be so kind as to tell me - and starting from Andres' LAN time and position, I then recomputed/derived all the Observer's positions at the various specified times listed by Gary. I have based my computation on the 300 kt south speed indicated by Gary. For each observation time given by Gary and each position deduced from my interpretation of Andres' results, I have computed what should be the Sun center geocentric apparent height (and also Azimuts) values, thus getting for each position and time a "computed height" directly comparable to Gary's published height for the very same time. I repeated this calculation over the entire 25 shot set and published my results to be independently verified by anybody in the community.
    So I am just (again) requesting that all my published results be independently CROSSCHECKED AND VERIFIED ON THE FOLLOWING POINTS :
    a - Is my understanding of Gary's published height as being "Apparent Geocentric Sun Center coordinates" correct ? I believe so, but if I have totally misundertood Gary's helful comments in [NavList 10013], then all this lenghty post and all the lenghty computations and work which are behind it are totally useless and VOID. The END !!!
    b - Is my own interpretation of Andres's results correct ? This point essentially covers the fact that apparently the data published by Gary seem to be an almost perfect parabola. I already have had kind direct exchanges with Andres and I am sure he will explain this to me. Thank you in advance Andres.
    c - Assuming that my interpretation of Andres's results is correct, could somebody crosscheck that my 25 subsequent positions derived for the 25 times of Gary's observations are in accordance with Andres' results ? This is a rather simple crosscheck and I thank whoever will do this.
    d - Assuming that all these 25 positions recomputed from Andres's results are correct, could somebody (else?) crosscheck that from the 25 positions obtained at the times of Gary's published observation times the Geocentric heights I am computing are correct ? Bigger task and Thank you to whoever will do this also.
    To this point, and assuming that my computations so far have been all correct, I come to the necessary conclusion that there can be NO MATCH between my reconstructed data and Gary's published data.
    Apparently and - according to my interpretation of Andres's results - Gary's published data seem perfectly symmetrical (a 2nd degree parabola) if considered from the Culmination time.
    >From the onset I have personnally felt that this feature seems highly improbable given the high N/S Observer's speed component. This personal view point is also supported by Jim's comment posted meanwhile in [NavList 10030].
    As a conclusion, and in addition to Peter Hakel's very same request in [NavList 10027], I would like very much that Gary be so kind as to publish the exact method he used to derive the data he submitted to all of us. The Data he published meanwhile with more significant digits [NavList 10035] are not sufficient for this purpose. Such full explanations by Gary will be a very welcome complement to this most interesting thread.
    Thank you very much in advance Gary, and Best Regards to you all from
    Antoine M. "Kermit" Couette
    NOTE 1 : Here "Hs" has the exact same meaning as "Ho" in Gary's data,
    NOTE 2 : ALL the question marks "?" appearing herunder are to be interpreted as symbols for "d" or "Degree". For definite lack of time, I only corrected the first line.
    NOTE 3 : Rightmost column should read "Gary's Data" (i.e. published heights Ho) instead of "Jim's data"
    Times Lat      Lon       Geoc. Ho    Azimuts    Gary's Published Ho's 
    17:00 N24d09'8 W078d30'0 Hs=42d18'1  Z=176.0d  Jim's data : Hs = 42d14'
    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'

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