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    Problem in equal altitudes of the sun around local apparent no on
    From: Mal Misuraca
    Date: 1997 Mar 10, 01:50 EST

            A problem in equal altitudes of the sun before and after local apparent noon,
    with consideration for error caused by movement of the boat. . . .
            A sailboat en route to Hawaii on August 3, 1995, in dead reckoning position
    28 degrees 24 minutes North, 143 degrees 22 minutes West, making course 231
    degrees true, speed 4.5 knots, makes the following sextant observations (GMT)
    of the lower limb of the sun on that day:
            21:09:00	77degrees 08.5 minutes
            21:19:09	78 degrees 12.8 minutes	
            21:25:04	78 degrees 33.4 minutes
            21:26:56	78 degrees 47.8 minutes
            21:30:30	78 degrees 58.1 minutes
            21:35:14	79 degrees 06.6 minutes
            21:39:00	79 degrees 08.8 minutes
            21:39:05	79 degrees 08.8 minutes
            21:39:10	79 degrees 08.8 minutes
            21:42:56	79 degrees 06.6 minutes
            21:47:40	78 degrees 58.9 minutes
            21:51:10	78 degrees 47.8 minutes
            21:53:10	78 degrees 33.4 minutes
            21:59:05	78 degrees 12.8 minutes
            21:09:05	77 degrees 08.5 minutes
            When the navigator realized at 21:39:10 that the sun had ceased to gain in
    altitude over the horizon and was hovering without apparent change in
    altitude, she began to reset her sextant to the exact altitudes seen before
    local noon and one by one recorded the time of the same altitudes after noon,
    as the sun descended.  She knew that the time half way between each set of
    paired altitudes was by definition local apparent noon.  This was a better way
    to fix the time of local noon than when the sun was hovering and she could not
    tell precisely when it hit her meridian (longitude) and thus made out local
    apparent noon.
            Three questions are posed.  First, what was the most probable time of local
    apparent noon (within 5 seconds) the navigator found?  Second, what was the
    boat's latitude and longitude fix for local apparent noon on August 3?  Third,
    what was the error in minutes of longitude for this fix for the fact that the
    boat was moving during this series of sextant shots?
            Anyone wishing to post an answer to these questions, please do so by March
    25.  The author's calculation will be published shortly thereafter, and the
    closest navigator(s) to the author's answer will be disclosed.  An explanation
    of the author's answer will be provided at length, so that all readers may
    examine anew this unique position-finding method, which requires only a
    nautical almanac and very simple calculations, with no spherical trig or sight
    reduction tables.  Finally, the author will compare the accuracy of the equal
    altitudes method to typical sight reduction methods, to see how equal
    altitudes stacked up.
                                    Mal Misuraca
                                    "Celestial in a Day"
                                    San Francisco, California
                                    "Passage East," Sausalito

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