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Re: Grenadine Lunar Distances
From: Arthur Pearson
Date: 2003 Feb 1, 21:10 -0500
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@LISTSERV.WEBKAHUNA.COM] On Behalf Of Fred Hebard Sent: Saturday, February 01, 2003 5:43 PM To: NAVIGATION-L@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