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    Data from three lunars, with some comments
    From: Fred Hebard
    Date: 2003 Jan 14, 14:55 -0500

    Below are some data on three lunars I took fairly recently, on dry
    land, together with calculated UT1s.  The decrease in precision
    between the first and the next two is interesting, and there was a
    surprise in the data for first one, so I thought the list members
    might want to see these.
    The altitudes were calculated from the known position, which was
    determined from a 7.5' topographic map.  The location was 36o46.6'N,
    81o51.0'W..  The sextant distances below have been corrected for
    index and instrument errors.  Correcting for semidiameter yielded the
    apparent distance between the centers (I also corrected for Jupiter's
    semidiameter, taking those sights on the edge of Jupiter, not its
    center).  The apparent distance was cleared for the effects of
    refraction and parallax by Young's method, as laid out by George
    Huxtable last year (I don't think George's implementation of Young's
    method corrects for anything else).   I made one extra iteration of
    George's formulas for refraction and parallax to determine those from
    calculated altitudes rather than apparent altitudes.  Greenwich mean
    time (ut1) was calculated by interpolation between distances
    calculated on the hour.
    date     obsvd,,,, sextant apparent cleared, date ,,, calc ,,, del Comment
    USA,,,,,,UT1,,,,,, o ,, ' , o ,, ' , o ,, ' , USA ,,,, UT1 ,,,, "
    Moon, Jupiter, Jupiter across Moon to lower limb
    12/27/02 06:21:43 052 24.9 052 08.4 051 18.6 12/27/02 06:22:02 19
    12/27/02 06:26:59 052 28.3 052 11.9 051 21.5 12/27/02 06:26:52 -7
    12/27/02 06:29:14 052 29.8 052 13.3 051 22.8 12/27/02 06:29:01 -12 6:29:14 1st
    12/27/02 06:31:17 053 31.1 052 14.7 051 24.0 12/27/02 06:31:05 -11 recorded as
    12/27/02 06:33:34 053 32.7 052 16.3 051 25.4 12/27/02 06:33:31 -92
    equivalent of
    12/27/02 06:35:36 053 35.0 052 18.5 051 27.5 12/27/02 06:37:07 +91 52o31.8'
    12/27/02 06:51:36 053 45.0 052 28.5 052 37.1 12/27/02 06:53:28 113
    12/27/02 07:03:34 053 52.5 053 36.0 052 44.8 12/27/02 07:06:30 177
    Moon, Aldebaran
    01/08/03 23:34:18 069 00.2 069 45.2 068 22.5 01/08/03 23:31:57 -141 may have
    01/08/03 23:36:19 069 58.1 069 43.1 068 20.1 01/08/03 23:36:48 29 had side
    01/08/03 23:38:43 069 57.5 069 42.5 068 19.1 01/08/03 23:38:56 14 error
    01/08/03 23:40:49 069 57.7 069 42.7 068 18.9 01/08/03 23:39:14 -94
    01/08/03 23:45:13 069 54.1 069 39.0 068 14.6 01/08/03 23:47:58 165
    01/08/03 23:47:49 069 54.7 069 39.7 068 14.8 01/08/03 23:47:30 -19
    01/08/03 23:50:58 069 53.1 069 38.1 068 12.6 01/08/03 23:51:52 55
    Moon, Sun
    01/11/03 20:24:11 104 53.3 104 24.5 104 01.6 01/11/03 20:26:20 129 considerable
    01/11/03 20:27:33 104 53.1 104 24.2 104 01.7 01/11/03 20:26:29 -63 side
    01/11/03 20:32:55 104 54.7 104 25.8 104 03.8 01/11/03 20:31:09 -106 error
    01/11/03 20:34:21 104 55.2 104 26.3 104 04.4 01/11/03 20:32:35 -106
    01/11/03 20:36:36 104 59.3 105 30.5 104 08.8 01/11/03 20:42:16 340
    01/11/03 20:38:28 104 57.8 104 29.0 104 07.5 01/11/03 20:39:24 57
    01/11/03 20:40:35 104 57.8 104 29.0 104 07.7 01/11/03 20:39:55 -39
    The 12/27/02 sights were my first lunar, although I had been working
    up to taking these data for months with altitude sights.  Note that
    the 6:29:14 distance was recorded as 52o 31.8', corrected for sextant
    errors, but this clearly was a blunder.  While collecting the
    subsequent data, I thought it likely that the real value was 52o
    29.8', due to reading the scale backward; I had been doing that when
    recording the sun's diameter off the scale.  Making this change fit
    the data extremely well so I left it.  I'm aware the validity of this
    is subject to challenge.
    I checked the 12/27/02 data (and the others) by plotting the observed
    distance against the time of observation.  I was stunned and
    delighted by how well the data fit a straight line (and one expects
    this line to be straight over short intervals), with an R^2 of better
    than 0.997.  I then picked the best observation, one that was most
    centered on the regression line, and used that to compute time with
    Bruce Stark's tables.  This was the 6:31:17 observation.  The time
    came in at about 12 seconds behind UT1.
    These data convinced me that my newly purchased Husun sextant was
    worth repairing rather than reselling (the handle was burst apart by
    leaking batteries), and encouraged me to explore further.  But I'm
    not so sure I would have felt that way if the data had been from the
    1/8/03 or 1/11/03 sights.  Here there was considerable variation, and
    I was quite careful to read the scale correctly.   Against Aldebaran,
    the moon goes into retrograde motion several times!  I feel good that
    the average error of the Aldebaran lunar is about 1 second, but it
    has considerable variation.  In the 1/11/03 sights, the data get even
    worse, with the mean time off by 30 seconds.  From the scatter in the
    data, it may be luck that I got this close.
    I think there were several things going on that explain some of this
    variation.  I believe the main factor was that in the Jupiter sights,
    the moon was fairly low in the sky and Jupiter not very far away, so
    I only had to tilt the sextant about 45 degrees, whereas in the other
    two sights, the bodies were directly overhead, making it much more
    difficult and fatiguing to hold the instrument steady.  Also, for the
    Jupiter sights, the moon was fairly new, so not too blinding and with
    low glare.  The moon was fuller for the next two lunars, and the
    Moon-sun sights had very high glare due to the sun.  For the
    moon-Aldebaran sights, the sky was hazy with high cirrus clouds.  In
    the moon-sun sights, one of the horizon-mirror mounting screws on the
    Husun was loose and side error was increasing alarmingly, whereas it
    had been steady earlier.  The moon-sun sights led me to dare testing
    those screws and tighten the loose one.
    Another factor was George Huxtable's "Evil Effect of Moon's
    Parallax."  The hourly change between the bodies was 35.3', -29.8',
    and 27.0 for the three lunars in date order.  So the moon was
    appearing to move almost 1/3 faster away from Jupiter on 12/27/02
    compared to the sun on 1/11/03.
    Another surprise was in store when I developed computer methods so I
    could clear each individual observation rather than just one, without
    too much sweat.  In the 12/27/02 data, there was a strong degradation
    in accuracy in the later sights.  This had not been apparent when I
    plotted observed distance versus time and fit a straight line.  The
    12/27/02 data had all dropped right into place along the regression
    line, whereas the data for the other two sights were scattered all
    over.  Here, I think I may have been getting tired towards the end of
    the moon-Jupiter series, leading to the error, and perhaps the
    instrument was drifting.  I should have stopped sooner.  But the
    point is that I wouldn't have noticed this if I hadn't cleared each
    individual sight and calculated UT1 from it.  It could have been
    discovered in other ways, such as comparing the slope of the fitted
    line to that expected, but I didn't do that until after noticing the
    The exquisite precision of these 12/27/02 data was delightful
    (especially before I found the deviations discussed in the previous
    paragraph).  With biological field data, my usual fare, one is doing
    well to get the coefficient of variation, the ratio of the mean and
    standard deviation, under 100%!  These astronomical data were well
    under .1%.  It's been fun to work at an entirely different level of
    precision.  I might add though, that it's difficult to record data to
    such high levels of precision and to handle the numerous inputs into
    one sight.
    My precision and accuracy with altitude sights is increasing
    considerably with steady practice, to standard deviations of the
    difference between observed and calculated altitudes often under 0.5'
    and even 0.25', from earlier values in excess of 2' or even 10' or
    20'.  I think if one were doing this on a daily basis, one could
    become reasonably proficient.  But a newcomer doesn't just pick up a
    sextant and determine her location to within a half mile.
    Frederick V. Hebard, PhD                      Email: mailto:Fred@acf.org
    Staff Pathologist, Meadowview Research Farms  Web: http://www.acf.org
    American Chestnut Foundation                  Phone: (276) 944-4631
    14005 Glenbrook Ave.                          Fax: (276) 944-0934
    Meadowview, VA 24361

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