Mr.Campbell ,

By the sunset fix you can see that Noonan precompted for checking position by celnav which was normal operating practice. For sunrise , due the on first leg delay , Noonan had to recompute en route since sunrise o/b would originally have occurred at the Turn Off Point before going inbound for Howland. If having gone astray , Itasca would have been long before 1912 GMT be warned by radio , but on the contrary : before 1912 GMT there was not any sign of distress. That holds Noonan precisely knowing where he was when commencing the approach procedure. Do we have any indication about this statement in terms of air navigation ? Yes we have : without exact initial calibration of latitude , the sunrise point of time having been precomputed , we know that the precise LHA of sun was 90-03-50 , computed by H.O.208 , Tab. II by navigator himself. @** 175453 GMT sunrise time the GHA of sun was [(175453) x 15] - 180 deg = 88-43-15.** Thence, @ observed sunrise the longitude was : 88-43-15-W + 90-03-50-W = 178-47-05-W. The latitude was already contained in the precomputation by homework. Whatever pre-sunrise track was flown , great circle , rhumb line , any other initial point , From sunrise Noonan knew exactly where he was , given some decline from observation error. I do btw not comment for "make point" , if a computation is good you can safely follow I.Newton : Non fingo hypothesis.

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This is for you guys that may have been following this discussion and scratching your heads about what is going on. This post by Mr. van Austen provides the opportunity to show that his methodology is wrong by demonstrating a basic error that anybody should be able to understand.

Basic to all computations for celestial navigation is knowing the position of the body being observed, in this case the sun. Celestial positions are specified like locations on earth. On earth the position north and south of the equator is called latitude and the location east and west of the Greenwich Meridian is called longitude. For celestial bodies, the position north and south of the equator is called declination and the position west of the Greenwich Meridian is called Greenwich Hour Angle (GHA.) Since the earth turns, the GHA of the sun increases at the rate of fifteen degrees every hour, one degree every four minutes and one minute of GHA every four seconds. This is why accurate time is so important because if your chronometer is wrong by just four seconds you will take out a value for GHA from the Nautical Almanac that is wrong by one minute of longitude which will make the derived position in error by one nautical mile.

In his post, Mr. van Asten states that at 17:54:53 GMT the GHA of the sun was 88-43-15 (88 degrees 43 minutes and 15 seconds. This is the same as 88° 43.2', rounded to the nearest 0.1'.) We don't have to take his word for it since it is easy for us to figure it out for ourselves by using the nautical almanac.

Look at the 1937 Nautical Almanac for July 2nd, available here:

https://sites.google.com/site/fredienoonan/resources/air-almanac-2009/sun-s-gha Take out the value of the Sun's GHA for 1800 GMT (the closest tabulated value to Mr. van Asten's time of 17:54:53) which is 89° 02.5'. Since this is the location of the Sun 5 minutes and 7 seconds after Mr. van Asten's time, we must make a correction for this difference. To do this we go to the Interpolation for the GHA of the Sun table available at the same site. Enter this table for the time difference of 5 minutes and 7 seconds and take out the amount the Sun moved in that time period which is 1° 16.8' of GHA. Since we are interested in finding the Sun's GHA for an earlier period, we must subtract this correction from the 1800 GMT tabulated value and find the GHA of the Sun, as tabulated in the 1937 Nautical Almanac (the almanac carried by Noonan), for 17:54:53 GMT was 87° 45.7'. Comparing this to Mr. van Asten's value of 88° 43.2' shows his in in error by 0° 57.5' equivalent to a 57.5 nautical mile error.

Check the math yourself:

GHA sun @ 1800 GMT = 89° 02.5'

Adjustment for 5:07 = - 1° 16.8'

GHA at 175453 GMT = 87° 45.7'

then:

van Asten's GHA = 88° 43.2'

Minus the correct GHA sun - 87° 45.7'

Deference = 0° 57.5'

This would also produce an error in the time of sunrise of 3 minutes and 50 seconds which we can also see by using the interpolation table to find the time interval that would produce the difference in GHA of 0° 57.5' .

Is that simple enough?

gl