NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: lunar parallax killed Amelia Earhart
From: Gary LaPook
Date: 2006 May 20, 13:27 -0700
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 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. 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:
From: Gary LaPook
Date: 2006 May 20, 13:27 -0700
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 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. 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/A3694854I 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.
