A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2010 Apr 3, 07:23 -0700
In reply to your post in [NavList 12672] Re: Sun Moon Lunars to 155 degrees,
YES you guessed it right about the "2 Body Method" I have kept using for the Position determinations from just the Lunar data.
Such "2 Body Method" is very well documented nowadays within our Community, and many people use it among us.
And as an a-parte, (hopefully not a "repeat" here to our Community, in which case I publicly apologize in advance),
... while I will never ever claim that I was the first one ever to have invented this "2 Body Method", I devised it from scratch in 1974, as well as its "3 Body Method" sister (using the Plans containing the Height Circles). I very painstakingly then computed all results (4 different full computations with just 3 bodies) through Log and Sine tables. It was my "personal research work" submitted during the Fall/Summer 1974 at the French Naval Academy.
This work was then officially rated as "Definitely innovative indeed .... BUT TOTALLY UNPRACTICABLE TO-DAY from any operational standpoint" ... just because of the then inexistent readily available computing power that we can find at any corner of any street nowadays. Many of my colleagues had lenghty smiles at me (to say the least) while witnessing and watching these endless computing hours. They all knew to well that I HATED computations with Sine and Log tables.
Having then the age of 21, I absolutely did not even care for or thought of disclosing any of these methods outside the French Naval Academy. My only preoccupation then regarding my own future was becoming an aircraft carrier pilot, and (quite almost) nothing else.
As regards the "3 Body Method" - and to the best of my current knowledge - first recent publication ever was done in the French Revue NAVIGATION by French Navy Navigation Professor Bodenez from France in 1976, THEN and ONLY THEN (around 1980/1981 if I remember correctly) in the US NAVIGATION review by M. George Kaplan from the United States Naval Observatory, then it was independently re-discovered by a number of people including in our Community at least Andres Ruiz ( Andres, you even re-discovered the "3 Body Method" on your own, am I right ?).
Careful research might demonstrate that both methods were already independently discovered much earlier than us all, (possibly M. Carl Friedrich Gauss ?) since it very often happens that in such occurrences, the exact same discoveries have been completed at different successive epochs and in various places by various different and good faith people. Just think of C.F. Gauss, Lobatchevski, and Bolyai : all these three mathematicians independently discovered non-Euclidian Geometry in our European history. Blaise Pascal in the XVII th Century in France re-discovered the now-called "Pascal Triangle" well known to the Chinese people Centuries earlier and the list of such examples is a lengthy one.
In view of your ongoing inquiries and questions about delta-T, I definitely need to clarify the method I am using when tackling Lunars.
Starting just from the published Distance and the 2 Heights, I compute both the UT of the Distance and the Observer's position according to the precepts of the "2 body method". This computation is performed through an INDEPENDENT SOFTWARE software using modern French BDL Theories. No use of any other software, therefore no use at all of Frank's computer at this stage.
As recently explained, since I am using modern theories with ET-TDT/TT as their main time variable - all 3 variables are fully equivalent and interchangeable for our current Lunar Needs - , I am to keep publishing every single time the delta-T value I am using, in order to help other NavList Members (Paul and David at least among possible members) to crosscheck results through their own independent calculations and publish them. The reason for my still on-going delta-T value indication apparently has kept being very clear to at least both of them.
Now, and only now does Frank's Computer comes to play as an additionnal and INDEPENDENT cross check.
We all know that we are to enter Frank's On Line Calculator with an assumed position. We also know that this "Magic OLC" gives the option of clearing lunars JUST from the Heights. In such case an assumed position STILL remains a requirement since - in such a "2 body" situation - it remains absolutely necessary to single out and choose the right position from a set of generally 2 possible ones.
When so using these 2 heights, Frank's OLC does indeed internally compute a derived position exactly through the "2 body approach" using the Lunar derived UT. IT DOES NOT DISPLAY THOUGH THIS INTERMEDIATE POSITION RESULT but only the final cleared distance, which is by all means the most primary task that we are expecting from it.
So, since in its "Heights using mode" this Computer does not display the intermediate position it has internally processed to complete clearing the Lunar, and if you need to know such "hidden" position, you are left with only trial and error, through entering successive positions in its "position only" mode and checking for the errors of the subsequently displayed cleared Lunar Distances. It can be a lengthy task but you should eventually reach the right spot, with the wonderful advantage that Frank's calculator is extremely user friendly and very fast ! I would bet that it is exactly the method that Brad has been following when just recently working the Aug 1773, 04 th Lunar Example if he determined such position just from Frank's on-line computer.
So, from my independently computed AND displayed position, I enter Frank's OLC in its "position only" mode (i.e. NO HEIGHTS entered), as well as with the EXACT UT value I found. I am therefore NOT adding any delta-T correction a second time when I cross check my results with Frank's computer.
This very last explanation should fully clear and settle this (in my sense no longer existing) matter between us since :
- in my initial computation with Modern Theories I HAVE to use delta-T, while as a courtesy to other members who use the same kind of Modern Theories I keep publishing every single time the delta-T value I am using, and
- when reworking my examples through Frank's Computer - which provides both of us with extra independent checks on results - I am not entering any second time any value of delta-T.
Regarding the heights determination which you covered, I see that we both are in absolute full agreement since - from the best determination/"guestimation" of their Anchorage site - we can see that the Sun is NEVER hanging over a clear sea horizon, and that - fortunately for us - the Moon most often is, as I explained in great detail in [NavList 12646] . In this specific case, we can therefore not and should not expect any top-notch accuracy on the Sun heights themselves.
One detail though : you seem to indicate that due North of the OHAMANENO Anchorage spot the horizon was limited just by the sea and apparently not by the land, which is not what I am able to see from Google Earth. So any clarification here will be most welcome, and please, be so kind as to post the island profile you mentionned. Until now, I have found and published that from this anchorage position unrestricted horizons lie only betweeen azimuts [175°-312°] and - [326°-338°]. Would you please be so kind as to independently cross check these 4 values. Thank you again !
AS A CONCLUSION
I will cover here and again an earlier view-point which should have been be made meanwhile more understandable and clear to all of us now :
- It is very well known that "just average" heights are more than enough to fully and accurately clear Lunars, and no question on that whatsoever, BUT
- if we want to get "MORE", i.e. attempt using such heights through the "2 Body" method to independently crosscheck the Observer's position, it really remains VERY REGRETTABLE that even when there under a clear horizon not obscured by land, the Observers then apparently did not take and record their heights to an accuracy better than probably some 5 arc minutes, as I could just recently deduce from the only very few moon heights (only 3 )in this example.
Best Regards, Happy Easter to you and let us all rest in Peace
Antoine M. "Kermit" Couëtte
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