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

**Re: First Moon-Star Lunar**

**From:**Antoine Couëtte

**Date:**2017 Dec 30, 19:20 -0800

*Dear Ed, Sean, and Frank,*

- Re:
- 1 - First-MoonStar-Lunar-EdPopko-dec-2017-g41011
- 2 - First-MoonStar-Lunar-SeanC-dec-2017-g41056, and :
- 3 - MoonStar-Lunar-EdPopko-dec-2017-g41062 , and

*Décidément* ... your First Moon Lunar, *Ed*, is raising a lot of interest.

*This time I have a question for you, Frank, directly related to solving this Lunar*.

Nonetheless, both *Ed* and *Sean* may react, since in setting up my upcoming twofold question to *Frank (see *7* further down) *, I am quoting "your" own numbers.

Fast Readers can proceed directly to ***4*** here-under, because I am doing a bit of "History" so that Lunarian Crazy Readers can get deeper into this subject.

***1***

*Quick recap* (Ref1) : This Lunar was shot from N28°41.2' W082°18.3' on Dec 24th, 2017 at 0h05m04s GMT . We have assumed that Height of Eye = 0', Temperature = 50°F and Sea Level Pressure = 29.92" Hg. *Ed* and *Sean* possibly worked in a slightly "Weather" environment, but this should be almost negligible for meaningful results comparison.

***2***

This Lunar was independently solved :

- First by
*Ed*through*Using Reed's algorithm in [his] HP calculator*" (Ref 1). Then : - By
*Sean*through "*using Frank's fomulae*" for Sean (Ref2) with his own derived starting data slightly different from*Ed's*. And finally : - Again by
*Ed*through his same method "*I input your updates and again used my calculator program based on Frank's workshop algorithm" .*

***3***

From what I have been able to understand -*and please Frank correct me if I am wrong here* - it looks that that *Frank's Algorithm *requires the following starting data :

*Moon Center and Aldebaran Geocentric heights, corrected for refraction*[and corrected for semi-diameter since we deal with Moon Center] , and named "" . And :*Ho**Moon Center and Aldebaran Topocentric heights*(i.e. as observed from the Earth Surface),*not corrected for refraction*[but corrected for semi-diameter since we deal with Moon Center], and named "" . And:*Ho+Corr**Distance from Aldebaran to Moon Center*(or better : to the "*Moon Center Best Determination*")*as seen from the Earth Surface and affected by refraction*, i.e. as measured through a "perfect and ideal" sextant able to "pick up" the exact refracted Moon Center. Such Sextant distance is named "". Finally :*LDpc*

Processing all these data through *Frank's Algorithm* yields a "*Cleared Lunar Distance*" named "** LDc**", which is the geocentric angular distance between the Moon Center and Aldebaran, thus directly comparable to Nautical Almanac derived data.

***4***

*Post Ref 2 by Sean definitely triggered my immediate attention* since it looks that through a fully classical method - as I understand *Frank's Algorithm* is - and from almost the very same starting data than *Ed's*, *Sean* was able to get a different *Cleared Distance* than *Ed*. And interestingly enough, when reworking this Lunar with the same data as *Sean*, *Ed *did not get the exact same Cleared Distance as *Sean*.

*This gave me the idea of solving this Lunar through the Classical Lunar Formulae I have been using from time to time in the past 6 years or so.* These are the* Chevalier de Borda's* Formulae I referred to in a recent post. *At least I believe them to be so*, and if I am wrong, please *Frank *be so kind as to correct me here and please be so kind as to let me know *who* published them first. Let's then call these ones "*B Formulae*" . As you can see in the enclosure, these are "straight brute force" Formulae.

Let's also call *Frank's Algoritm* - as used by both *Ed* and *Sean* - the "*F Formulae*" .

I am not familiar at all with "*F Formulae*".

**I decided to compare the results of "B Formulae" with "F Formulae" and I decided to check them against results very close from Frank's On Line Calculator results.**

***5***

And ... *lo and behold* ... I just discovered this afternoon that "*B Formulae*" and "*F Formulae*" require exactly the same starting data in order to yield the Cleared Lunar Distances. Are they [closely] related ? Let us see :

**Ref 1 Lunar computations by Ed**

- Moon Ho+corr = 37°07.3' Aldebaran Ho+Corr = 36°12.0' LDpc = 95°38.7' Moon Ho = 37°50.1' Aldebaran Ho = 36°10.7'
*"F Formulae"**Ed's LDc = 95°04.5'*"B Formulae" results LDc = 95°04.709'**Difference "F Formulae" - "B Formulae" = -0.209 '**

**Ref 2 Lunar computations by Sean**

- Moon Ho+corr = 37°07.8' Aldebaran Ho+Corr = 36°12.1' LDpc = 95°38.6' Moon Ho = 37°50.1' Aldebaran Ho = 36°10.7'
*"F Formulae"**Ed's LDc = 95°04.8'*"B Formulae" results LDc = 95°05.097'**Difference "F Formulae" - "B Formulae" = -0.297 '**

**Ref 3 Lunar computations by Ed from the very same data as Sean's**

- Moon Ho+corr = 37°07.8' Aldebaran Ho+Corr = 36°12.1' LDpc = 95°38.6' Moon Ho = 37°50.1' Aldebaran Ho = 36°10.7'
*"F Formulae" Ed's LDc = 95°04.9'*"B Formulae" results LDc = 95°05.097'**Difference "F Formulae" - "B Formulae" = -0.197 '**- Difference between
*Ed*and*Sean*working from the same algoritm and onto the same starting data : 0.1' .

***6***

A bit surprised at these results, I decided to check how "*B Formulae*" would perform against my own "Big" Lunar Software - let's call it "*C Formulae*". Here are the relevant data derived through "*C Formulae*" as follows :

- Moon Ho+corr = 37°07.416' Aldebaran Ho+Corr = 36°12.001' LDpc = 95°38.576' Moon Ho = 37°50.048' Aldebaran Ho = 36°10.679' . And :
**C Formulae LDc = 95°04.746' .**Note**:***Frank*, I am think that your On Line Calculator results are extremely close (to better than 1") from these "*C Formulae*" results.

- I then ran "
*B Formulae*" with the data immediately here-above :**"***B Formulae*" results LDc = 95°04.741'**Difference "C Formulae" - "B Formulae" = +0.005 '**

I also found that ** Frank's On Line Computer LDc = 95°04.7' **(probably very close from 95°04.75' as suggested here-above).

***7***

*Hence my two-fold question to you Frank :*

- Since
*Ed*and*Sean*do not get the very same LDc from identical data (Ref 2 and 3),*what is the exact LDc yielded by your own Algorithm in this specific case when processing such Ref2 or Ref3 data? And :* *How do the so-called "*Borda's Formulae*" in the enclosed document relate to your own Algorithm, and are they safe for use under any and all Configurations ?***I have obtained my "*Borda's*" results through electronic "brute force" computation.- Maybe this could explain some differences between your upcoming results should your Algorithm require some "manual computation" steps as it seems to be the case.

Thank you very much, *Frank*, for your* Kind Attention* and for your reply.

Meanwhile .. ** Happy New year again to all** !

*Antoine Couëtte*