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    Re: My first Lunar
    From: Kent Nordström
    Date: 2008 Jul 24, 19:04 +0200

    Frank quoted me [5727]: And you wrote:
    "I have started looking at your LD prediction program and, in due time, I
    will run my test cases in your model to compare. It should be rather
    interesting because I think I have a rather good precision in my way to
    No YET you don't. But undoubtedly soon you will. :-)
    I have now made a comparison between Frank's model and mine and here are the 
    results. In all cases I have used my own way to compensate for 
    oblateness/flattening. By using my data in Frank's modell error in lunar and 
    and error in longitude are read out.
    Case              Error in lunar  Error in longitude
    1                    0'                                        1.0'
    2                    -0.3'                                    10.3'
    3                    0.3'                                     9.6'
    4                    0.6'                                     19'
    5                    0.1'                                     3.3'
    6                    0.4'                                     11.1'
    7                    -0.2'                                    5.5'
    8                    0.1'                                     1.8'
    Mean             0.125'                                 7.7'
    Std. Dev.       0.3'                                     6.1'
    So it seems to me that my model is rather good. The deviations are probably 
    that I model e.g. refraction and oblateness/flatness in a different way from 
    Even if I am a little late I give my results to Jeremy's first lunar 
    directly taken from my model (case 8 above):
    -     GMT: 22-19-32
    -         moon true altitude: 66d 09m 00.9s
    -         Jupiter true altitude: 45d 13m 56.3s
    -         Cleared distance: 68d 13m 04s
    -         Longitude: On Jupiter:W 61d 53.7m, on moon W 61d 44m
    -         Latitude: N 14d 33.5m
    George Huxtable wrote [5897]: Actually, Kent and I agree about that 
    correction, when working a lunar with maximum rigour. My edition of Raper 
    dates from 1864, and in that, it's table 53, "Correction of the lunar 
    distance for the contraction of the vertical
    semidiameter". Perhaps Kent will confirm that's what he is referring to.
    That's used, just as it says, to correct the measured distance for the
    apparent vertical shrinkage of the Moon, and that certainly does depend on
    the difference in refraction between the Moon's centre and limb. Indeed, I
    took a look at that table, and noted that for all Moon altitudes above 30º,
    it would be less that 1", so disregarded it. So in this case, (unlike for
    the corrections to altitude, above) that correction really was a matter of
    being right in principle but numerically trivial. But it isn't to be used
    when correcting for altitudes above the horizon.
    I enclose a scanned copy of the tables, for which I have used the 
    corresponding algorithms in my LD model. Hopefully at least one of them is 
    exactly or near exactly to table 53 in Raper 1864, that George uses. These 
    are Swedish tables so I take the liberty to try to translate into English.
    Tabell XXV: Moon's augmentation (hope I got that correct?)
    Tabell XXVI: Decrease of the SD for the sun and the moon due to refraction 
    (here George and I disagree). Arguments are apparent altitude and the angle 
    between the distance and the object's vertical.
    Tabell XXVII: Correction to the altitude for calculation of the moon's 
    parallax in altitude due to oblateness/flattening. Arguments are moon's 
    azimuth and latitude.
    Tabell XXVIII: Correction to the moon's eqv. HP due to earth 
    oblateness/flatness. Always minus. Arguments are moon's HP and latitude.
    Tabell XXIX: Moon's parallax in azimuth due to earth oblateness/flattening. 
    Arguments are moon's azimuth and latitude.
    Tabell XXX: Correction to the LD for the moon's parallax in azimuth. The 
    idea is to use a value from table XXIX and then enter into tabell XXIX. Note 
    that here you have to use the angle between the distance and the vertical. 
    Further, also one's position - latitude north or south - and the direction 
    of the moon and the other object have implication on the sign for this 
    correction. Venster=left, höger=right.
    Andrez Ruiz wrote [5845]: In Lunars this equation is approximate to avoid 
    the use of the azimuth, removing the 3rd order terms by:
    PA = HP * COS( H ) * (1-(sin(B))^2/300).
    I agree that the involvement of the moon's azimuth may complicate things. 
    What I can see the expression from Andrez is always positive while my 
    corrections are positive if the azimuth is >90d, else negative.
    Kent N
    ----- 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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    File: 105932.tables.ppt
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