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RE: EdPopko-dec-2017-g41011  , and see also : Couëtte-dec-2017-g41034
 
Dear Ed,

In further reference to both posts listed here-above, it is easy to use Frank’s Calculator ( http://reednavigation.com/lunars/lunars_v4.html ) to compute your published Aldebaran Lunar. We just need to rearrange your exact initial data in order to adequately feed Frank’s Calculator.

In order to get the required Topocentric Sextant heights including refraction with Height of Eye = 0' for Aldebaran and for the Moon Lower Limb, I simply did the following :

Sextant Observed heights, no Instrument error, including refraction with Height of Eye (HOE) = 0' :

Moon :      Ho + Moon Corr - (SD+AUG) = 37°50.1' - 42.8' - 15.1' = 36°52.2'
Aldebaran : Ho + Aldebaran Corr       = 36°10.7' + 01.3'         = 36°12.0'

Hence we now need to enter Frank's Calculator with :

Dec 24th, 2017, GMT 00:05:54, Moon Height 36°52.2' , Aldebaran Height 36°12.0', and Distance to Far Limb 95°53.8' with T = 50°F and Sea Level pressure = 29.92" and set to 0 both Longitude and Latitude in the upper window.

You will get :

Error in Lunar: 0'
Approximate Error in Longitude: 0° 01.0'

*******

I keep advocating performing iterations with Frank's Calculator to get the best out of it.

In order to compute and publish his "Approximate Error[s] in Longitude", Frank is using a very simple rule as follows which will let you easily correct "backwards" for your Sextant Star to Limb Distance :

1 - 0.1' = 6 " , and :

2 - Since the Moon Right Ascension varies 0.5" / second of time, then 0.1' = 6 " is equivalent to 12 seconds of elapsed time to get a change of 0.1' in the Moon RA, and :

3 - Given that it takes 4 seconds of time to get a Celestial Body GHA change of 1', in 12 Seconds of time, the Moon GHA has changed by (12 / 4)', which translates into a difference in "Moon Longitude" alongside the Equator equal to 3' (here we ignore the 0.1' change in the Moon RA).

4 - Hence we have the following well known approximate "standard" ratio : 0.1' of sextant distance error equates to 3' of Longitude error, or better stated for our current study : 3' of Approximate Longitude error translate into 0.1' of sextant distance error ( i.e. the well known "30 to 1 ratio" )

Hint ! This "standard" ratio is only true under the most favorable cases when the other Body is close to the Moon Vector speed [against stars]. Most often, 0.1' of Sextant Distance error equates to much more than 3' Longitude error. This is why Frank very wisely advises us that his stated Longitude Error is only an Approximate [or better : "Optimum Configuration"] Longitude Error.

And this is also the main benefit of performing iterations with his Calculator : it enables one to easily derive the "actual" ratio vs. the "standard" one.

5 - To conclude, with the "standard" ratio of 0.1' in Distance to Limb Error being equivalent to 3' in Longitude Error, from the published "Longitude Error" it is easy to derive a much more accurate Corrected Sextant Distance value with the following Correction rule : 1' of Approximate Longitude Error equates to 1/30 ' of Sextant Error.

*******

Let us use this "standard ratio" for your case. Since Frank says Approximate Error in Longitude: 0° 01.0' , such Error translates into a Sextant Error of (1.0 / 30)' = 0.03333 '

Simply correct your initial Sextant Distance by 0.03333' in the right direction. Here given the geometry of the sight, we need to subtract 0.03333 ' from your initial Sextant Distance Value.

Then run again Frank's Calculator after having modified only the Sextant Distance into 95°53.767' (vs. 95°53.800') and this time you get :

Error in Lunar: 0'
Approximate Error in Longitude: 0° 00.1'

The fact that your "Approximate error in Longitude" has now come to show ALMOST zero indicates to you that the " 30 to 1 standard ratio " is in fact the actual one for this Lunar observation. NO need then in this case to continue iterations. It is a rather rare occurrence.

However, should wish to just mathematically fine tune your results, let's subtract 0.1' / 30 = from 95°53.767', i.e let's run again Frank's Computer with Distance = 93°53.764' (vs. 95°53.767') and we get this time :

Error in Lunar: 0'
Approximate Error in Longitude: 0° 00.0'

Hence you have observed here under the most favorable geometric configuration, with Aldebaran being extremely close from the instantaneous Moon Speed Vector against stars. This result is telling you that given your other unchanged data, your actual distance read in your sextant with no error should have been 93°53.767' (or even 93°53.764' for Math crazy Kermit).

Ed, in your post EdPopko-dec-2017-g41011, you stated :

QUOTE :

GMT from Lunars vs Actual Time of Observation
  00:06:26  GMT lunars calculated
  00:05:54  GMT lunars actual observation
   00:00:32  GMT calculated vs actual

UNQUOTE

You computed - hopefully with no error - and obtained your results here-above through an approximate computing rule, with 32 seconds of clock error translating into a little more than 1.0' Sextant Distance error.

Frank's Calculator is much more accurate, and in turn you actually performed very much better then : you actually observed with less than 0.1' Sextant Error on your Star to far Limb distance !

To conclude, your actual sextant error in this case is well below 0.1'  (0.0333 '   !!! ), and your Longitude Error is just 1.0' . Well done, Ed, it is a magnificent achievement !

Best Friendly Regards, and thanks again to you Frank for your wonderful Calculator.

Antoine Couëtte