NavList:

Dear Frank,

Thanks for the detailed answer. I would like to emphasise same aspects where (I suspect) I was misunderstood.

I strictly separete observation/sextant errors from software errors. I don’t expect 2” or 3” accuracy from my sights. I have taken hundreds (maybe even thousands) of lunar sights. And I am still doing this regularly;  it is something like meditation for me. Therefore I know very well what are the practical limits of observation’s accuracy. If I achieve final 0,2'...0,3' accuracy - it is a very good result.  

When I wrote that I would be happy the software error being equal or less than 0,05’(3”) my considerations were quite intuitive. I simply presumed that it would be nice the errors being under sextant’s limits (I will later return to this aspect). For example here is an analogy: the values in Almanacs and sight reduction tables are published with accuracy of 0,1’. But no one expects traditional altitude measurement from natural horizon with such an accuracy, because the horizon itself can produce larger uncertainties (0,5’ or even more). This means that values are published with higher accuracy than needed for altitude sights.   

 You, wrote: “I can't recall if you have ever specified the magnification of the telescope on your preferred sextant. Let's suppose is a four-power scope.”   

I always use 7X telescope with very excellent optics for lunars. Of course, everything you wrote about the possibilities to visualy identify small angles is true. But this is more complex question. You described Jupiter lunar to proof that it is not possible to identify very small angles. I have experience that the possibility to identify small angles depends on more factors. For example, let’s compare 3 lunar sets taken under ideal conditions:

1) Sun lunars;

2) Venus lunars;

3) Star (1,0 magnitude) lunars.

Which set of observations most probably will be the most accurate (I am talking only about the observer’s ability to check tangent point)? Usually the most accurate will be Sun lunar set. The Venus lunar most probably will be the worst. Why? Because two limbs (the Sun and Moon) allows us to see the overlaping part of limbs, when they are close to the tangent. But the bright spot of Venus ir so amorph that it is hard to expect high accuracy.

We are talking about ability to see small angles through the telescope of sextant. I can see a round landmark from my appartment. If I sit in a chair, look throug the window and measure the same angle (I am measuring the diameter of this object) dozens of time, the micrometer readings differs only 0,1’. That means I am off by +/-0,05’ (or +/-3”). With other sextant the results are +/-0,1’ (6”). And all this is repeatably constant. (I am not talking about the absolute value of measured angle, but only how much measured angle values differs one from other).

Other example: when I measure Sun lunars (let’s say 6 measurements in the set) under ideal conditions, the difference between each individual measurement from the average error for this particular lunar set usually is about +/-0,05’.

Of course this is not the final accuracy of the measured sextant angle, because the measured angle contains index error inaccuracies, arc error inaccuracies etc. The mentioned value only expresses the ability to visualy fix the tangent point. It is very hard to achieve the same results with Jupiter or Venus lunars.

The all above mentioned is an explanation how I get 0,05’ desired value for software. As you can see all my assumsptions are not scientifically based, but only emotionaly based.

Frank, your explanation relating to the Moon’s limb imperfection is great! I did not know that these values reach +/-3” ( I thought they does not exceed 1”). Thanks! Very interesting indeed!

You also wrote about your lunar calculator : “It's always possible that there's still a bug somewhere in my code that I missed, but right now this information is not worth much. Can you provide a specific example? “        

Here are some examples. Position: 57°N; 26°E; 10°C; 1010mbar

1) Sun-Moon near limbs; 30.04.2023; 16:20:00; Frank’s distance: 120° 28,59'; Paul’s Lunar4.4: 120° 28,77'; Difference: 0,18’.

2)Capella-Moon near limb; 03.05.2023; 19:20:00; Frank’s distance: 114° 58,44'; Paul’s Lunar4.4: 114° 58,58'; Difference: 0,14’.

But on 30.04.2023 Marss, Pollux and Regulus lunar distances differs only 0,01'...0,05'  from Paul's Lunar4.4. As you had mentioned maybe there is still some bug in your calculator. 

Modris Fersters