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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Did the International Date Line cause the loss of Amelia Earhart?**

**From:**Gary LaPook

**Date:**2011 Mar 22, 03:19 -0700

The short answer is that she got it exactly wrong. Using the wrong date for STAR sights would have made them overshoot the island by about 60 NM in longitude, not undershoot by that amount as she theorized. However a one day error would only change the position of the sunline landfall LOP by 2.7 NM so any problem with the star lines would have been cured by the first sun shot.

I sent the following series of messages to her with attachments.

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I read your website and it is quite interesting and I followed your computation but that is not the

way a navigator does it. We use Greenwich Hour Angle (GHA) to determine the positions of

bodies and this is directly tabulated in the Nautical Almanac and the Air Almanac for the sun,

planets and the moon. To determine the GHA of a star we find the GHA of Aries in the almanac

and add to it the Sidereal Hour Angle (SHA, the inverse of R.A.)

I have also been analyzing Noonan�s navigation for about ten years now. I am an ATP and have

been doing celestial navigation in airplanes since 1977 and I have ferried planes across the ocean

using a sextant.

I an afraid that this is going to be embarrassing for you but you need to know about the errors in

your website. .

First, the date line is an imaginary line and you do not have to do anything when you cross it, you

can keep any date you want until you touch shore where it becomes convenient to get on the

same date they are using ashore. See the discussion at:

http://www.fer3.com/arc/m2.aspx?i=115629&y=201102

You talk about "local time" but flight navigators have no use for local time. It is different on a

ship where the ship�s clock is changed by even hours at convenient points, when traveling east or

west, so that the ship's watches can be adjusted to keep in synch with the approximate local

apparent solar time and lunch can be served at approximately local noon. Time zones are 15

degrees wide, 900 NM at the equator, 450 NM at 60 degrees latitude. A ship sailing westward

near the equator at 12.5 knots will cover 900 NM, one time zone, every 72 hours so will set the

clock back one hour at noon every third day and this will keep the ship�s clock approximately in

step with the position of the sun. The same ship traveling westward at 60 degrees latitude will

reset the clock twice as frequently. In the days prior to time zones the ship�s time was reset to

noon each day at the noon observation. As Captain Aubrey said when looking through his

sextant, �Make it noon� and then the hour glass was turned and eight bells were sounded starting

the first afternoon watch.

Flight navigators do not reset their clocks while in flight so none of that applies to them. Noonan kept his chronometers set to GMT. By his reckoning he took off at 0000 GMT

on July 2nd and planned to arrive at Howland at about 1800 GMT July 2nd and these would be the

times he used to look in his Nautical Almanac, not much chance for confusion here, no reason to

look at the next date�s data in the Nautical Almanac. Likewise on a ship, the ship�s chronometers

will be kept on GMT. However, the ship�s navigator doesn�t take the ship�s chronometer on deck

to time his celestial observations so he may set his wristwatch to local ship�s time by comparison

to the chronometer. He then uses the �Zone Description� (Z.D.) to convert his watch time to

GMT. (I am disregarding any watch error or chronometer error in this discussion but the

navigator will allow for them as part of the normal computation procedure. See the top of the

form at:

https://sites.google.com/site/fredienoonan/other-flight-navigation-information/modern-bygrave-sl

ide-rule/NauticalAlmanacForm.pdf?attredirects=0 )

For the sake of argument, assume Noonan kept his watch on Lae time. The Zone Description at

Lae is minus ten hours (-10). This is the amount you must adjust your Lae watch time to find

GMT time and date. At the takeoff, Lae time was 1000 (10:00 a.m.) on July 2nd. Apply the -10

hour Zone Description by subtracting ten hours from Lae time and you find GMT of 0000 hours

and the date remains July 2nd. Eighteen hours later Lae time was 0400 (4:00 a.m.) July 3rd. and

you must subtract the same ten hours (since you have not changed your watch time, your watch is

still keeping Lae time, Z.D. is still -10.) Since you can�t subtract 10 from 4 you must borrow a

day, 24 hours, from July 3rd, and just like normal subtraction, when you borrow the day from July

3rd your reduce it by one day to July 2nd, You add the 24 hours to the time of 0400 making the

time 2800 (28:00) on July 2nd, and then subtract the ten hours (-10 Z.D.) and you still get 1800

GMT on July 2nd. This is the standard way navigators deal with time and Noonan had done this

same computation thousands of a times as a ship�s navigator. You can see how extremely

unlikely it would have been for Noonan to use the wrong date in the Nautical Almanac especially

since he certainly kept his chronometers set to GMT. It is also quite likely that Noonan

precomputed all of his landfall approach celestial data the night before they took off, or early in

the flight, for twenty minute intervals from 1800 GMT to 2400 GMT July 2nd so that he could

prepare a graph of the computed altitudes. See:

https://sites.google.com/site/fredienoonan/topics/precomputed-altitude-curves

To do all of these computations and to draw the graph would take less than one hour. If you look

at his chart notations on the California to Hawaii and on the Natal to Dakar charts you will see

he marked the times of the LOPs in GMT but Earhart kept her journal on the time at the

departure point.

Assuming that he did use the wrong date then he would have had a longitude error of 59.1

minutes of longitude, 59.1 NM at the equator, for LOPs derived from taking observations of

STARS, so you are almost correct about this. You point out the discrepancy between the �200

mile� and the �100 mile� out position reports, claiming that crossing the dateline between these

observations caused Noonan to use the wrong date data accounting for the discrepancy. But,

Noonan would have noticed such a large discrepancy himself since there had to be an error

somewhere and he would have checked his computations. Such a large divergence in positions

would have required a 120 knot wind shift between the fixes which is obviously impossible.

Where you are completely wrong is in claiming that using the wrong date would cause the same

longitude error (60 NM) when shooting the sun for the LOPs for the landfall approach. See:

https://sites.google.com/site/fredienoonan/topics/landfall-procedure

and: https://sites.google.com/site/fredienoonan/discussions/navigation-to-howland-island

All you have to do to see this is to look at the Nautical Almanac for July 2, 1937 which I posted

here:

https://sites.google.com/site/fredienoonan/resources/nautical-almanac-1937/almanac-1937-22.JP

G?attredirects=0

Look at the Sun�s GHA (Greenwich Hour Angle) column, the third column, and compare the

values for the same times but for July 2nd and July 3rd. For example, at 1800 GMT on July 2nd the

sun�s GHA is 89̊ 02.5' and for the same time on July 3rd the GHA is 88̊ 59.6'. The difference

between these values is only 2.9' so if Noonan had used the GHA for July 3rd then the error in

longitude would have been only 2.9' which is 2.9 NM at the equator, not the 60 NM that you

claim. This slight difference is caused by the eccentricity of the earth�s orbit which causes its

orbital speed to vary resulting in solar days that are not exactly 24 hours long. This resulted in a

change in the equation of time between July 2nd and 3rd ,as can be seen by looking in the first

column in the almanac, from 3 minutes, 50.2 seconds to 4 minutes, 01.4 seconds and this 11

second change results in the 2.9' change in GHA and in the 2.9' error in longitude.

I think where you go wrong is in not recognizing the difference between GMT and Greenwich

Sidereal Time. A sidereal day is only 23 hours, 56 minutes and 4 seconds compared to the 24

hour solar day. This 3 minute and 56 seconds difference accounts for the 59.1' shift in the

positions of the stars but doesn�t effect the position of the sun for navigational purposes since its

position is determined by GMT not GST.

I have posted many reference documents that you might like to look at concerning the navigation

of this flight.

See:

https://sites.google.com/site/fredienoonan/

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Second message:

You might like to look at how celestial navigation is actually done in flight at these links:

https://sites.google.com/site/fredienoonan/other-flight-navigation-information/ocean-navigator-article-1

https://sites.google.com/site/fredienoonan/other-flight-navigation-information/working-the-sight-in-flight

https://sites.google.com/site/fredienoonan/other-flight-navigation-information/in-flight-celestial-navigation

http://www.avweb.com/news/avtraining/IFR_bySunAndStars_200781-1.html

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Third message:

If you look at the format of the 1937 almanac you will notice that both July 2nd and July 3rd are on the same page. So Noonan would be doing his computations and as the hours progressed he moves down the page through the July 2nd values. Then, as he crosses the date line and for his next sight he suddenly drops down to the next day giving up his orderly progress through the July 2nd data? I don't think so.

I have also attached excerpts from the current Air Almanac.

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Fourth message:

I have attached the July 2&3 pages for 2009. Since 2009 is the year after a leap year and so is 1937 you can use the 2009 data for 1937 to an accuracy of a couple of minutes of arc in declination and GHA. I have also attached GNC 20, Global Navigation Chart, scale of 1:5,000,000, ten times the scale of a sectional so you can use the same plotter.

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Fifth message:

I have attached the July 3, 2009 and the March 2, 2011 Air Almanac pages. If you compare the GHAs of the sun for July 2nd and 3rd you will see that they differ by only 2.8' making any error in the computed longitude from using the wrong date the same 2.8', 2.8 NM at the equator.

The calculation of GMT and Greenwich date that I described before is done every time a surface navigator (with his watch set to ship's time) takes a sight and has nothing to do with crossing the date line so Noonan would have done it thousands of times while he was a mariner. I will give you an example. Right now it is 7:03:22 p.m. (1903:22), March 1, 2011 in California. If I took a sight right now, to use the almanac I would have to find out the GMT and date for right now. The Z.D. in California is + 8 now ( +7 when on daylight saving time). The math goes like this. 1903:22 plus 8 hours makes the time 2703:22 GMT, March 1, 2011. Since this exceeds 24 hours we know we must reduce the time by 24 hours, making 0303:22 GMT and carry a day and add that to March 1st making the Greenwich date March 2nd. Anytime you take a sight in California after 4 p.m.requires that you advance the date by one day to find the Greenwich date and do this calculation.

Going further by referring to the almanac pages I have sent you we can find the declination and the Greenwich Hour Angle (GHA) of the sun. The almanac gives the declination of the sun at 0300 GMT, March 2nd as 7� 22.4' south and the GHA is 221� 56.0'. Looking at the interpolation table for the extra 3 minutes and 22 seconds shows the GHA increased 51' making the GHA of the sun at 0303:22 GMT as 222� 47'. (No interpolation is necessary for the declination since it is listed every ten minutes in the Air Almanac. When using the Nautical Almanac, which only tabulates data every hour, you do the same type of interpolation for declination.) Note that neither Right Ascension nor Greenwich Sidereal Time, nor local sidereal time enters into this calculation.

I have also attached the Air Almanac pages for July 26 & 27, 2009. There are some dates during the year were the equation of time does not change from one day to the next so using the wrong date will have no effect on the computed longitude from a sun shot. Compare the the GHAs of the sun on these two pages and you will see that they are exactly the same so using the wrong date would have absolutely no effect on the resulting computed longitude.

If you have any questions just let me know.

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Sixth message:

I wrote to you before about the errors in your website. I agreed with you that a one day error in

using the almanac for a a star sight would lead to about a one degree error in longitude (actually

59.1') but I didn�t point out the direction of that error. I am attaching three pages from the 2009

Air Almanac, July 2nd, July 3rd and the interpolation table for GHA. We can use the 2009 almanac

for computations for 1937 since these years are at the same point in the leap year cycle so, for the

sun there is very little difference in the data (a few minutes of GHA and declination), and for

stars there is a constant difference of 33.2' in GHA and calculated longitude. We can use these

pages to do a sample calculation to see how the error works out. Using your example of Antares

crossing your meridian at 1728 GMT on July 2nd. (This is not the way a navigator would find his

longitude since a navigator cannot measure when the body crosses his meridian. Your method

can only be used for a telescope at a fixed location with the polar axis aligned with the meridian.

Navigators have traditionally measured the sun�s height at local noon, when it reaches its highest

point in the sky, but this observation is for latitude, not longitude, because the exact time of noon

cannot be determined this way as the sun�s altitude changes very little in the minutes around

noon so the actual change in altitude is lost in the noise of the measurement. From a moving

aircraft or fast ship the point of highest altitude is never the point where the body crosses the

meridian as the movement of the vessel causes the altitude of the body to change and this effect

swamps out the actual change in altitude of the body. To find longitude navigators traditionally

measured the altitude of a body on the �prime vertical,� bearing straight east or west. ) We can

use your example, however, to demonstrate the effect of using an incorrect time or date on

finding longitude since an error in time has exactly the same effect on longitude for any LOP.

Using your example, we find our longitude by determining the longitude of the body when it

is crossing our meridian at which point it has the same longitude as we do. The longitude of

the body is called Greenwich Hour Angle (GHA) and we can find this number in the almanac for

any time and date. Looking at the page of the Air Almanac for July 2nd, 2009 to find the position

of the star Antares at 1728 GMT we first take out the GHA for �Aries� which is the reference

point, the zero or prime meridian, for the positions of stars. The distance west from Aries to the

body is called Sidereal Hour Angle (SHA, the inverse of Right Ascension.) and adding the two

quanities, GHA Aries and SHA of the body gives us the GHA of the body, its longitude, and our

longitude if it is crossing our meridian.

The GHA of Aries at 1720 GMT was 180̊ 52.8'. Then we must use the interpolation table to

account for the increase in GHA during the extra eight minutes. The earth turns two degrees in

eight minutes (see interpolation table) and we add this two degrees and we find the GHA of Aries

at 1728 GMT is 182̊ 52.8'. We then find the SHA of Antares from the same page which is 112̊

30' , the same as a R.A of 16 hours 30 minutes. ( I don�t know where you got your R.A. of 16h

46m since it is not that now and in 1937 the SHA was 113̊ 35.8', a R.A. of 16h 25m 37s. The

difference between 1937 and now is due to precession of the equinoxes.) Adding the GHA of

Aries to the SHA of Antares results in a total of 295̊ 22.8' for the GHA of Antares at 1728 GMT

on July 2, 2009. This would make our west longitude the same, 295̊ 22.8' . Since longitude is

measured only up to 180̊ east and west we would convert this west longitude into east longitude

by subtracting it from 360̊ resulting in a longitude of 64̊ 31.8' east. (Somehow you came up

with a west longitude so there is some error in your calculation.)

Then to see what happens when the wrong date is used for the calculation we can do the same

computation for July 3rd by starting with the tabulated GHA for Aries which is 181̊ 51.9' at 1720

GMT. To this we add the same 2̊ from the interpolation table and the 112̊ 30' SHA and the

result is 296̊ 21.9' GHA of Antares resulting in a west longitude of the same number, 296̊ 21.9'

west. Compare this computed west longitude with that for July 2nd and we find that the computed

longitude is 59.1' further WEST. (Normally we would convert this to an east longitude of 63̊

38.1' east but this does not show the change as clearly as talking about only west longitudes. The

longitude calculated on July 3rd is 59.1' less east so that means it is 59.1' further west.)

The crux of your theory is that if Noonan had erroneously used the data from the July 3rd page

that he would have calculated that his longitude was one degree, 60 NM, further east (and closer

to Howland) than he actually was and so turned too soon, 60 NM west, to search for Howland

which prevented him from finding the island. The computation I just did shows that using data

for a star sight that is one day after the true Greenwich date actually results in a calculated

longitude that is about one degree further west than the actual position of the plane, exactly the

opposite of your computation. This is because the GHA of Aries and of all stars increases (moves

further west) by 59.1' each day so all longitudes calculated from star sights also move further

west every day by the same amount.

In my previous email I showed that the longitude of a sun line would not be this much in error

but would be only 2.7'. Look at the GHA for the sun at 1800 GMT on both days and you will see

that the GHA on July 3rd is 2.7' less meaning that the sun was 2.7' further east at the same time.

So a sun line LOP would indicate to Noonan that he was 2.7' further east than his actual position

so would have him flying 2.7 NM further west along the LOP while searching for Howland. This

would not make a significant difference especially in light of the fact that Itasca was making a

smoke trail that blew downwind at least 10 NM, well past the erroneous coordinates for Howland

that many think he was using and much further than this additional 2.7 NM theoretical error.

If you have any questions, just let me know.

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Seventh message:

We know that Noonan set his chronometers to GMT (G.C.T.) from a letter that he sent to P.V.H. Weems describing a prior Pacific crossing. This letter was published in "Air Navigation" by Weems (1938.) See page 423.

https://sites.google.com/site/fredienoonan/resources/weems/weems-422-423.JPG?attredirects=0

We also know he used the Greenwich Hour Angle method of computation that I showed you in my prior posts. See page 425

https://sites.google.com/site/fredienoonan/resources/weems/weems-424-425.JPG?attredirects=0

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8th message:

To summarize my prior messages. In the very unlikely event that Noonan erroneously used the data for July 3rd near the end of the flight for star sights he would have calculated a longitude about 59 NM west of his actual position which would then cause him to overshoot Howland. This is exactly the opposite of what your theory predicts.

I also pointed out that any longitude error from the star sights would be cured by the subsequent sun observation as the error from using the wrong day's data for sun sights is only 2.7 NM, not the 60 NM error that you theorized.

If you have any questions, just ask.

Gary LaPook

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