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    Re: lunar parallax killed Amelia Earhart
    From: Gary LaPook
    Date: 2006 May 20, 15:06 -0700
    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 (H P) of the moon at that time was 59.2' from the above almanac page which would make the largest possible error in the moon LOP also 59.2 NM which is what that web site alludes to. But that parallax is only if the altitude of the moon was horizontal or zero degrees. To find the actual correction that must be applied to the sextant altitude (and the size of the error if you forget to apply it) you must multiply the horizontal parallax by the cosine of the observed altitude of the moon. When you do this you find that the error in omitting this "parallax in altitude" (P in A) 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 74º 27' so the P in A correction was still only 15.8' or 15.8 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. This very same table is also found in all the commonly available tables of the time including HO 211, HO 214, Weems Line of Position Book , and in table 34 of  Bowditch  going back at least as far as 1927. It as also quite possible that this table was in the 1937 Nautical Almanac but since I do not have a complete copy of it I do not know for sure. This table does not incorporate a correction for semi diameter since it is for use with a bubble sextant such as Noonan was using.

    Another, possible, reason that Noonan was unlikely to make this mistake is that a P in A correction table was printed on each daily page of the Air Almanac based on  the moon's H P for that particular day. I say that this is "possible" because I do not know whether Noonan was using the Air Almanac or the Nautical Almanac for his computations. The inventory of equipment found in the plane after the Luke Field accident lists the 1937 Nautical Almanac but Noonan could have obtained a copy of the 1937 Air Almanac before the second departure several months later since it was being published by his friend P.V.H Weems

    For those only familiar with the Moon correction table in the Nautical Almanac it is not obvious how much of the total altitude correction is due to the P in A  correction because it is not broken out separately from the refraction and semi diameter corrections. In aviation celestial practice these corrections are handled separately with a common refraction table for all bodies including the moon, sun, stars and planets and the daily pages P in A table for the moon. Semi diameter is not applied for the sun or the moon when using the bubble sextant since you are actually sighting on the center of the body, not its lower or upper limbs as done with a marine sextant.


    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 61' down to 54'.

        


    Paul Hirose wrote:
    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:

    http://www.bbc.co.uk/dna/h2g2/A3694854
      
    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.


    No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.392 / Virus Database: 268.5.6/340 - Release Date: 5/15/2006


    Paul Hirose wrote:
    Royer, Doug wrote:
    Were the
    head winds grossly miscalculated? Thus putting them grossly out of position
    and/or consuming much more fuel than they calculated or allowed for.

    The speed line they obtained from the Sun rising nearly dead ahead
    should have revealed any serious headwind, and Noonan could have shot
    course lines out his side window during the night.

    Itasca observed 7 knots of wind from the east.

    There seems to have been enough fuel. According to the Itasca's radio
    log, at 1912Z Earhart said "We must be on you but cannot see you." She
    had enough fuel to fly until 2400Z.


    A scan (about 750 k) of one of the planning sheets is on the web:
    http://gemini.lib.purdue.edu/Earhart/EarhartDisplay/Name.cfm?ID=484
    (The direction is backward because the flight was originally going to
    circle the world eastbound. After the delay due to the takeoff mishap,
    they decided to reverse the direction.)

    Modern coordinates for the beginning and end of the flight are:
    Lae              06 44 S 147 00 E
    Howland Island   00 48 N 176 38 W

    Using those coordinates, my GPS agrees with the planning sheet data to
    practical accuracy. (The speeds and distances on that sheet are in
    statute miles.) But look at those 15 waypoints on a great circle track!
    It seems a pointless refinement for a flight so close to the equator. I
    would eliminate all those little course changes, and plan the flight so
    Earhart could fly a constant magnetic course all the way from Lae to
    Howland.

    Though I'm skeptical about the lunar parallax theory, the author of that
    page does have a good point: the Moon was available. But its altitude
    may have been too high for convenient use. When Earhart said, "we must
    be on you," it was about 65° high at Howland. I don't know if Noonan
    would have been able to shoot it.

    By 2100Z the situation would have improved, with the Sun and Moon both
    about 45° up, and a 125° split in azimuth.

    It is interesting that the ships on station were able to receive some of
    Earhart's calls but couldn't communicate with her radio. And how well did
    her radio-direction finder really function? Was it calibrated and did she
    really understand how to use it?

    According to that paper by radio engineer Hooven, "The people
    responsible for installing the radio equipment and instructing Miss
    Earhart in its use reported that they had difficulty in retaining her
    attention, and it became obvious as the flight progressed that she did
    not understand the frequency limitations of her direction finder, nor
    how to make proper use of it."

    Hooven also said Itasca's skipper received no clear instructions on
    exactly what radio assistance was expected, and never got any
    acknowedgement that the information he sent to Earhart ever reached her
    before takeoff.

    Here is the title and authors of the book I read about this. It's
    very good
    in technical and historical detail (although nothing is proved or
    finalized). It most likely is at your public library as that is where I
    picked it up.

    "Amelia Earhart: The Mystery Solved"

    Elgin and Marie Long

    Thanks for the tip. I was at a library Friday, but the book was checked
    out. (Their catalog showed Elgen, not Elgin, for the author's name.) If
    I ever get hold of it I'll post a book report.


       
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