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    Re: Grenadine Lunar Distances
    From: Arthur Pearson
    Date: 2003 Feb 1, 21:10 -0500

    Fred, and Herbert,
    
    Many thanks for your analyses and observations. Comments and
    clarifications:
    
    * The Ds values I listed are the uncorrected sextant distances BEFORE
    index correction or any other correction. Same story for the altitudes
    listed.
    * I believe the above clarification implies that Herbert's analysis of
    the Jan. 10 lunars indicates an average error of 1.4' vs. the 2.3' I
    cited. My figure was for the 4th observation alone which is the only one
    I solved (my solution has now been corrected as noted below).
    * The discrepancy in the altitude of the moon in the Jan. 10 lunar
    (second series) revealed serious flaw in my spreadsheet calculations.
    This affected only the moon altitude, but its impact on the results was
    material. I now agree that the moon's altitude was 36� and rising (not
    17�). This changes my solution for GMT to 18:40:42, 1min 55sec fast for
    a distance error of 0.9' (originally incorrect figure was 2.3').  Fred's
    reckoning was 2min 28sec fast. This is a big improvement either way.
    * Regarding hourly rate of change in distance: for the Jan. 10 lunar I
    got 21', Herbert 24', Fred 27'. I still get 21'/hour, but this is for
    the apparent distance after correction for parallax and refraction. For
    the geocentric distance, I get an hourly change of 28' for the Jan. 7
    lunar, 27' for the Jan. 10 lunar. This seems to explain the difference
    with Fred, still not sure with Herbert.
    * Fred states that my error implies a gap in contact. As the distance
    was increasing, round limb facing west and GMT per lunar was greater
    than truth, I believe that my measurement was too large and that I had
    an overlap rather than a gap. My confidence on this point was shaky
    until I consulted the table to this effect on p. 290 of Bruce Stark's
    book.
    * Having both of you point it out, I now see that I could well have a
    systematic error in my instrument or my technique. Finding it would be a
    big step forward. I'll look at my past data and try some stellar
    distances.
    
    I am genuinely grateful for your analysis and comments. I can't imagine
    a more productive, collegial environment for improving one's technique
    and understanding of lunars and their subtleties.  Many thanks to you
    both.
    
    Sincerely,
    Arthur
    
    
    
    -----Original Message-----
    From: Navigation Mailing List
    [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM] On Behalf Of Fred Hebard
    Sent: Saturday, February 01, 2003 5:43 PM
    To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    Subject: Re: Grenadine Lunar Distances
    
    Arthur,
    
    Thank you for sharing these data with us.
    
    I calculated GMT for each one of your observations, using your known
    position to calculate altitudes of the bodies, rather than the
    observed altitudes you had for your first set of observations.  The
    calculations were made using Young's method, as laid out by George
    Huxtable on this list.
    
    The mean and standard deviation of the difference from the lunar GMT
    to the true GMT were 259 plus or minus 240 seconds for the first
    lunar and 192 plus or minus 62 seconds for the second lunar.  The
    GMTs from both lunars were fast.  When I omitted the first
    observation, an obvious outlier, from the first set, its mean and
    standard deviation decreased to 170 plus or minus 56 seconds.  So the
    precision of both lunars was similar (and not all that shabby), but
    they were about 3 minutes fast, implying a gap in contact of 1.5' of
    arc.  It is hard for me to imagine what might be causing this error,
    but it would be nice to track down.
    
    Comparing the lunar GMTs of the individual observations from which
    you made calculations,  for the first lunar, I had a GMT of 19:44:59
    versus your 19:44:55.  The difference may be due to you using
    observed altitudes to obtain refraction whereas I used calculated
    altitudes.  For the second lunar, I had a GMT of 18:41:15 versus your
    18:42:59.  By my reckoning, you were "only" 2 minutes, 28 seconds of
    time fast, rather than 4 min, 12 secs, implying a longitude error of
    37 minutes.
    
    I also would like to note that my calculations indicated that the
    moon would be changing relative to the sun by 28' of arc per hour
    during the first lunar and 27' of arc during the second, which may be
    different from what you indicated.
    
    Again, thank you for sharing these data with us in such a gracious
    manner.  I hope you see a need to return the Caribbean soon to gather
    more data!
    
    Yours Truly,
    
    Fred Hebard
    
    
    

       
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