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    [Fwd: Re: lunar parallax killed Amelia Earhart]
    From: Gary LaPook
    Date: 2006 May 19, 13:07 -0500

    -------- Original Message --------
    Subject: Re: lunar parallax killed Amelia Earhart
    Date: Fri, 19 May 2006 01:52:38 -0700
    From: Gary J. LaPook <glapook@PACBELL.NET>
    Reply-To: Navigation Mailing List <NAVIGATION-L@LISTSERV.WEBKAHUNA.COM>
    References: <8F3B43F188FC6B45B8184C5FFC0B84A6128115@def-mail.remecrds.corp>

    Gary LaPook adds:
    This web page has some of the basic navigation wrong.  First it states that the moon passed 20º south of Howland at 7:01 am (1831Z) when, in fact the moon passed NORTH of Howland at 1837Z and its altitude was 76º 56' at that point since its declination was 13º52' North. See http://www.geocities.com/fredienoonan/almanac-1937-85.JPG

    The horizontal parallax of the moon at that time was 59.2' from the above almanac page. But that parallax is only if the altitude of the moon was horizontal or zero degrees. To find the correction that must be applied to the sextant altitude you must multiply the horizontal parallax by the cosine of the altitude. When you do this you find that the error in omitting the "parallax in altitude" correction only comes to 13.4' which is the same as 13.4 nautical miles. Also, if Noonan had omitted this correction then the plane would have been 13.4 NM north of where he thought it was so it would have been able to find Howland by following the sunline on a heading of 157 T.

    At the time of their last transmission at 1912 Z the altitude of the moon was 75º 41' so the P in A correction was still only 15.1' or 15.1 NM and the azimuth of the moon was 328º T so omitting the correction would still place them north of the island.

    However it is very unlikely that Noonan could have made this mistake since the navigation table he was using, HO 208, Dreisenstok, has the "MOON" correction table on the very first page, just inside the cover, and this table incorporates the parallax in altitude correction with the refraction correction. Adjacent to this table, and on the same page, is the table for "Sun or Star" which only has the refraction correction. These very same tables are also found in all the commonly available tables of the time including HO 211 and the Weems Line of Position Book going back at least as far as 1927. This table does not incorporate a correction for semi diameter since it is for use with a bubble sextant such as Noonan was using.

    BTW, the horizontal parallax is calculated by taking the arc sin of ( the radius of the earth, 3440 NM, divided by the distance to the moon.) Since this distance varies during the month  from 196,164 NM to 218,954 NM  the H.P. varies from 60' down to 54'.

    This web page speculates that Amelia Earhart and Fred Noonan missed
    Howland Island because Noonan failed to correct for parallax when he
    shot the Moon:
    This web page speculates that Amelia Earhart and Fred Noonan missed
    Howland Island because Noonan failed to correct for parallax when he
    shot the Moon:
    I believe Noonan precomputed his sight reductions (that's what I would
    do), so if he did make that mistake, it would have happened on the
    ground. A blunder that big seems unlikely, though.
    The 1939 edition of "Practical Air Navigation" (U.S. Department of
    Commerce publication) has a Moon altitude correction table. It's much
    like a modern table. You go down the left-hand column to find altitude,
    then move across until you come to the column corresponding to the
    Moon's parallax in altitude. The tabulated value at this point is the
    combined parallax, refraction, and semidiametor correction.
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