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Note te Frank : I have unsucessfully attempeted to register as "amc1753". How 
should I proceed ?? Thank you for your kind attention and understanding.

Antoine

Aug 08, 2009


Dear Jeremy,

Please find hereunder full results pertaining to your Moon Observations as I 
would present them to our community. See preliminary results 05 Aug 
hereunder.

First, thank you for confirming us the exact meaning of the "ON the Arc" 
instrument correction, which I had surmised right, as also George Huxtable 
had the kindness of pointing out directly to me.

I have used 2 completely different methods to process the data of your example.

1st Method : LAN (or LAM as you have it :-) )
Revised results are extremely close from the ones I had posted here 3 days ago, and show as follows:

Moon Transit south of Moving observer occurs at 09h51m39s7 UT2 (0.1 second apart from previous results)
Observer's position at that time is : N2149.5E13003.7 (same position) with 
SDEV equal to 0.5 NM, which yields an observed Latitude accuracy of +/- 1.0 
NM at 2 sigmas and a Longitude error  of 3.8' at 2 sigmas.
SDEV defines the dispersion of errors around the "ideal values" in case there 
would have been no observational error at all.

The remarks concerning Moon Declination "speed" and Observer's SMG South 
component being almost equal, both effects even each other out and for this 
reason (Observer's speed being still slightly greater), UT of Culmination 
occurs only 2.9 seconds of time after UT of moving observer 's meridian 
transit.

Therefore, positions at requested times will remain unchanged, namely :

At 09:00 UT (18:00 LT) , DR position was  N2200.8E13006.5 as reckoned from the 
09h51m39s8 observed Moon fix
At 10:00 UT (19:00 LT) position was N2147.7E13003.2 DR, same as above
At 11:00 UT (20:00 LT) position was N2134.5E13000.0 DR, same as above.

2 nd method : brute force processing of all your 33 LOP's (Marcq Saint Hilaire's Method)

Method 2A

For time 09h51m39s7 UT2, with all 33 LOP's I again find exactly the same observed position, i.e. :
N2149.5E13003.7 with SDEV equal to 0.5 NM (same definition for SDEV). All 
intercepts fall within +/- .8 NM of running fixes (and therefore no 
unrealistic/unreasonable single observation)

Method 2B

Process the observations 3 at a time, which leaves us with only 11 LOP's to 
process. At time 09h51m39s7 UT2, I find a very slightly different position :
N2149.6E13003.7 with SDEV equal to 0.4 NM (same definition for SDEV). All 
intercepts fall within +/- .7 NM of running fixes with - therefore - no 
single set of observation out of reasonable range either. In this case, SDEV 
has slightly decreased down to 0.4 NM vs 0.5 NM, which is very sensible since 
processing 3 Observations at a time - and treating them as a single 
observation - necessarily smoothes out some of their individual 
"distortions".

Note on Method 2 A and B.
At this step, I would not carry out any deeper statistics (through attempting 
for example to remove some unknown systematic observation error) because all 
observations fall within a very  narrow azimuth range (175.1 ? - 183.9?) 
which would definitely render such results totally meaningless.

OVERALL COMMENTS :
Well, I am impressed by a few facts :

-	The quality of the horizon as seen from a height of 107 ' (From which ship 
BTW ? ) Had you had the possibility of observing from a lower altitude, you 
would have got even better results.

-	The quality and consistency of all your 33 observations, including the quick 
turn-around time between some of them (some 30 seconds of time only between 2 
successive shots, which I personally consider a quite good achievement)

Additional notes : The quantity of data to process in your example ( some 350 
numbers to type/enter !!!! when NO single error can be tolerated ) is about 
the maximum you can realistically process if you do not have automatic data 
transfer from both your sextant and your Chronometer to your numbers 
crunching computer.

This might explain why so few of us have accurately responded to your 
"challenge", which surprises me (just) a little, but I appreciate that I am 
quite new to this Wonderful Forum (Attaboy ! Frank)

As in all cases, longitudes derived from sextant observations can be only as 
good as your exact knowledge of UT2. If it were 4 seconds of time off, then 
your longitude will be 1 arc minute off, while your latitude will not have 
changed by any significant/appreciable amount, event with such a "fast moving 
declination" Moon. Temptation is sometimes to use GPS time as a value for 
UT2. This is no longer possible since no leap seconds govern the GPS time 
which therefore has stayed much more stable than UT/ UT1/2.

What we now are expecting are your own published results from your GPS 
observations. I have always thought that GPS is a GREAT opportunity to 
Celestial Navigation since when you use it as DR position, it immediately 
calibrates the overall quality of your own observations.

Best Regards, and Thank you again. Read you soon

Antoine

Antoine M. Cou?tte

******************************************************

Aug 05, 2009


Dear Jeremy,


Subject to double checking my computation - which I have not done yet - and 
working through your example, and assuming that "0.8 arc minute on the arc" 
means :" from instrument value uncorrected for error, substract 0.8 arc 
minute to get such value corrected for error ", I would suggest the following 
results, with TT-UT = 66.0 Seconds of time :


UT of Moon Culmination as seen from moving observer : 9h51m42,6s

Diffrence between Culmination and Transit times : 2s8 . The observer has a 
definite speed towards south ( 13.16 kts south speed component), but - 
interestingly enough - the moon has a declination decreasing by almost the 
same value, as its declination goes 12.85 '/hour towards the south. Therefore 
it explains why both effects almost cancel each other out. This is why both 
Culmination and Observer's True Meridian transit are so close, by only 2.8 
seconds of time.

UT of Moon transit observer's Meridian (i.e. Moon passing due south of moving 
observer) : GMT 9h51m39s8, or LT = 18h51m39s8

Position at time of Moon Transit trough crossing observer's meridian :
N2149.5E13003.7 (sorry I am using Air Navigation Computers notation, since I 
am an Airline Pilot, which means : 21?49'5 N , and 130?03'7 E )

SDEV of measures is 0.6 NM, which gives a Latitude error of 1.0 NM with 2 
sigma and a longitude error of 3'8 with 2 Sigmas.

At 09:00 UT (18:00 LT) , DR position was  N2200.8E13006.5 as reckoned from the 
09h51m39s8 observed Moon fix

At 10:00 UT (19:00 LT) position was N2147.7E13003.2 DR, same as above

At 11:00 UT (20:00 LT) position was N2134.5E13000.0 DR, same as above.

LAST POINT : If I have made Instrument corrections the wrong way, then I need 
to rework your example with instrument corrected values higher by 1'.6 than 
the one I have used. As a consequence, with the assumption that this 1'.6 
angle change should/will have no significant effect on both Parallax values 
and Refraction values as well, then Observed Latitudes will be 1'6 to the 
south and Observed Longitudes are unchanged by reference to indicated 
positions hereabove.


Just be so kind as to confirm me that I have done Instrument error removal in 
the right direction. I somewhat unfamiliar with the terms "ON the Arc" and 
"OFF the arc".

Thanking you for your Kind Attention and Awaiting your reply, I ma remaining,


Most Sincerely Yours


Antoine M. Cou?tte


One last question : With such a Height of eye .... where have you been 
observing from ? an Aircraft Carrier upper deck ? (e.g; USS John F. Kennedy 
114 ft !!! )

----------------------------------------------------
[Sent from archive by: antoine.m.couette-AT-club.fr]


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