A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2017 Dec 27, 00:42 -0800
RE: EdPopko-dec-2017-g41011 and see also : Couëtte-dec-2017-g41034
In further reference to both posts listed hereabove, it is easy to use Frank's Calculator ( http://reednavigation.com/lunars/lunars_v4.html ) with your own exact initial data. We just need to rearrange them. In order to get the 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 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 only 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"
You will get : Error in Lunar: 0.1'
Approximate Error in Longitude: 0° 02.5'
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 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 RA change of 1', in 12 Seconds of time, the Moon Greenwhich hour angle has changed by (12 / 4)', which translates into a difference in Longitude equal to 3' .
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 : 3' of 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 in 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 Longitude error.
And this is also the main benefit of perfoming iterations with his Calculator which can very easily show the "actual" ratio vs. the "standard" one.
5 - To conclude, with the "standard" ratio of 0.1' in Distance to Limb being equivalent to 3' in longitude, from the published "Longitude error" it is easy to derive a much more accurate Sextant Distance value with the following 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° 02.5' , such Error translates into a sextant error of (2.5 / 30)' = 0.08333 '
Simply correct the initial sextant value by 0.08333' in the right direction, here given the geometry of the sight, we need to substract 0.08883 ' from your initial Sextant Distance Value. Then run again Frank's Calculator afyter having modified only the Sextant Distance into 95°53.717' (vs. 95°53.800') and this time you get :
Error in Lunar: 0'
Approximate Error in Longitude: 0° 00.0'
The fact that your "Approximate error in Longitude" is actually 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.
Hence you have observed here under the most favorable geometric configuration, with Aldebaran being close from the instantaneous Moon speed agains 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°53.717' .
Ed, in your post EdPopko-dec-2017-g41011, you stated :
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 !
To conclude, your actual sextant error in this case is below 0.1' (0.0833 ' !!! ), and your longitude error is just 2.5' . Well done, Ed, it is a magnificent achievement !
Best Friendly Regards, and thanks again to you Frank for your wonderful Calculator.