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    Re: Lunar Calculation Presentation
    From: Modris Fersters
    Date: 2022 Sep 8, 11:26 -0700

    Hi, Edward Falk again!

    You wrote: Frankly, I very much doubt that in real life, I could read lunar distance with a sextant to the accuracy that would make this method worthwhile.”

    Why do you think you would’t be able to measure lunar distances with appropriate accuracy? I have made hundreds of such measurments and I can say that I don’t find them more complex than typical vertical altitude measurements. For example I recently had quite strange experience with the usual Sun sights. For some period I had no opportunity to take the Sun sight with the sea horizon as reference (I used an artifical horizon for long time). And I took a lot of lunars. But when I at last took a standart sight I found it more complex then lunar distance measurment :))

    And I can say that I dont feel that my experience with lunar sights has changed very much during the time. Of course, some first attempts maybe were a little bit unusual, but one can get used to it very quickly. As I have documented all my sights, I can say that the error is typicaly in range 0…0.4’. Some worst results are off the true values 0.6…0.7’ (but this rarely happens).  And I have tested it hundreds of times.

    Obviously lunar sights should be made with the all possible accuracy. And there are some rules that are to be taken into consideration. If these rules are ignored you will never reach the accuracy of some tenths of minute of arc.

    I will try to write down the most important rules (maybe I will forget something, then sorry). I will not describe each position in detail to be maximum compact.

    *Use appropriate sextant. Plastic ones will not answer the accuracy requirements. Only a good metal sextant must be used.

    *Use sextant’s main arc correction values, if you have a certificate (I did not have certificate for my SNO-M sextant, therfore I had to finde the arc errors by myself). The arc errors may easily reach 1’ (it depends on sexstant model). If you know micrometer errors – applay them too (these errors may reach 0.3' or even more. Usually the users don’t no that there is such an error). Even filters may cause the additional errors.

    *Always turn micrometer in one direction (on final adjusment) to avoid backlach error. And this must be done also during index error check.

    *Always check the index error of the sextant using Star (in this case make the horizon mirror a slight side error) or by the Sun. Index checking by horizon is not so accurate.

    *If your sextant has adjustable telescope, always check the paralellism of the telescope axis to the sextant plane. If this is ignored there will be an additional error. This error will be grater on large angles.

    *Always make contact of the images of the Moon and the Object in the central part of the field of view of the telescope (in the zone between the two vertical paralel wires, if your telescope has them). If this is ignored there will be an error, especially measuring large angles.

    *If your sextant has, let’s say, 4x and 7x power telescops, use 7x power. Some users don’t like inverting telescops, but for lunars they are very good (for example, I use such a telescope).

    *Don’t try to adjust the Moon and the Object precisely. Just make the two images overlap a little bit or make a little gap between them (it  depends on the motion of the two objects: whether they are seperating or are getting closer). And then wait a moment when the two objects are in contact (tangent to the limb of the Moon).

    Easy method to find the the Moon and the Sun in the telescop view: look in lunar prediction tables for aproximate geocentric lunar distance on the full hour of Universal Time closest to your observation time. You can use, for example, Frank Reed’s online Lunar Distance Almanac link here. Average the tabulated value to nearest full degree. Set the sextant to this angle. Look at the Moon through the sextant’s telescop and rotate the instrument along telescope axis. At the moment when sextant's plane will be perpendicular to the Moon’s horns you will find the Sun in the field of view.   

    You wrote: I've also been reading Huxtable's "about lunars" which uses Borda's method, and that doesn't seem quite so bad”.

    Before you start to clear lunars with Borda method, you should answer a question to yourself: why do you need excatly this method. I do not recomend Borda method as a starting position. It is complex in paper format. The most inconvenient is interpolation which makes this method very time consuming.

    If you try real observations and want to check how accurate they are, I would recomend Frank Reed’s online lunar analyser link here. Just fill in your geographyc coordinats, time and date, temperature and pressure, your measured lunar distance and compare with calculated value. No altitude measurments are needed.

    If you are interested in historic paper format clearing methods (as I do) then you can study them. A lot of useful e-books you can find here.

    I have studied a lot of historical methods and found Thomson’s method the fastest one. Of course it does not allows corrections for temperature and pressure, but it is important only when celestial object’s altitude is low. But historically such observations were avoided.

    Historically highly valued were tables made by Joseph Mendoza y Rios  link here. This is method from the very begining of the 19 century. This metod was used for example by Franklin (the method was popular in british navy). I tried it and found it very convenient. All the process consists of some addition operations. I need about 8-10 minutes to clear lunars with this method.

    It was very interesting to read about the background of your interest in Lunars. My interest in lunars also began with HM bark “Endeavour”, when I accidently read an article about Cook’s first voyage where it was mentioned that there was no chronometer on board of the ship. And I started to study how they managed to get their longitude. Only later I found that all the great expeditions of the last decades of the 18 century and the first decades of the 19 century used lunar method to get longitude  (even if there was one or more chronometers on board). La Perouse, Flinders, Franklin, Vancouver, Krusenshtern etc, etc, etc.

    PS Sorry if I am off topic.  

    Modris Fersters

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