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    Re: Ex-Meridian Exercise
    From: Peter Hakel
    Date: 2010 Dec 31, 10:01 -0800
    During a private conversation on another subject Antoine suggested that I use a parabolic fit to Greg's ex-meridian data.  When I only processed the first four data points, thus extrapolating to LAN, the results were not crazy but not very good either.  The longitude was off by about 2 degrees (computed LAN came too early), the latitude was within a degree but still not as good as we'd like to see.  Then Antoine reminded me to include the fifth observation made at the computed LAN at UT=19:58:00.  Now the results were much better:

    December 27, 2010

    noon_curve.xls
    : (five data points, screenshot attached)
    Computed UT of LAN: 20:00:37
    Lat: N 34d 08.2'
    Lon: W 119d 51.7'

    noon_sight.xls: (treating the fifth point as LAN)
    UT of LAN: 19:58:00
    Lat: N 34d 10.2'
    Lon: W 119d 12.5'

    Antoine also suggested using the first and fifth data points for a standard two-LOP crossing:

    lops.xls and two_body_fix.xls (using the first and fifth data points):
    Lat: N 34d 10.2'
    Lon: W 119d 12.6'

    From Greg's GPS position taken as AP I calculate (with sun.xls and intercept.xls):
    #1    0.6A     172.3
    #2    0.4A     172.7
    #3    1.0A     173.1
    #4    1.0A     173.6
    #5    0.7A     180.0
    These results agree with Greg's quite nicely, I think; the azimuths are right on, the intercepts differ by up to 0.2'.

    My thanks to Greg and Kermit!


    Peter Hakel



    From: Greg Rudzinski <gregrudzinski@yahoo.com>
    To: NavList@fer3.com
    Sent: Mon, December 27, 2010 5:41:08 PM
    Subject: [NavList] Ex-Meridian Exercise

    Today was a fine Southern California winter day and perfect for this ex-meridian exercise that Byron Franklin has been talking about. Four standard LOP Sun lines were taken 28 minutes or so before the LAN. These same four LOP's were worked out as ex-meridians to provide a Latitude to cross each LOP at a very shallow cut (7°). The ex-meridians were reduced by Bowditch table 29 and 30 as well as by formula. There was a small difference between the two sets of reduced results but nothing to be concerned about. Shown by link is a plot of one example of the ex-meridian/LOP fix which to my great surprise was only 2.3 nautical miles from GPS. The three other observations were equally as good. So for those looking for a truly unique celestial challenge then try the ex-meridian/LOP fix shot. It was a lot of fun for me and I hope my working notes aren't too messy to follow. Notice the quality of the horizon in the linked photo. No excuses when looking at a sharp horizon like that.

    Greg Rudzinski
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