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    Re: Modern Lunars
    From: Antoine Couëtte
    Date: 2016 Sep 18, 10:15 -0700

    Hello to all,

    Initial Note:Thanks to a kind private note from Dave Walden, I have been able to significantly modify the enclosed [former] study on Lunars, in which I replaced the former words "errors" by the words "changes". This should contribute to a better understanding of the concepts I have addressed there. Thank you again very much, Dave.

    I joined NavList some 6 years ago, essentially because of your discussions on Lunars, a subject I had never studied before.

    I almost immediately studied Lunars from scratch on my own (no "Classical Methods" studied then) in order to tackle them with modern computation power. I became familiar with the Lunar "Classical" methods - and only a bit familiar actually - about one year ago.

    The enclosed document summarizes what I have been able to understand between 2 different methods of tackling Lunars:

    - the "Classical Methods" which use [GEOCENTRIC] CLEARED DISTANCES as benchmarks, and:

    - the newer methods which I am hereby calling "Modern Methods" which use [TOPOCENTRIC] SEXTANT DISTANCES [AFFECTED BY REFRACTION] as benchmarks. The effects of Refraction can be huge onto Lunars results and they must be addressed very carefully,  otherwise Lunars become totally worthless and useless.

    To the best of my knowledge, Classical methods are used by Andrés Ruiz, Peter Hakel, and Frank E. Reed (am I right about your on-line Lunar Computer, Frank ?).

    And it is interesting to notice that both Paul Hirose and Kermit independently developed recent "Modern" software using "sextant distances" as Lunar Benchmarks.

    Just one extract from the enclosed document:

    Although Lunars practical utility has totally vanished, modern computation power can tackle them with much greater efficiency: e.g. computing the Sextant “synthetic” Distances (i.e. the Distances which should be observed in a Sextant) and fine tuning successive UT1 values until the computed Sextant “synthetic” Distance matches the Sextant Observed Distance [e.g. to +/- 0.5”] enables solving any Lunar. Bodies’ Limb(s) constantly change shapes and refraction is also specific to each point of them. Classical Computations partially account for refraction through adding a limited number of corrections to the Bodies SD’s, but cannot match modern computation results and reliability. The latter - ALONE - can accurately compute the minimum distance between the ever-changing distorted Limbs under ANY configuration through considering the Sextant synthetic distance as the angular distance between the distorted Limbs measured alongside the unique Great Circle perpendicular to both of them. Modern methods can also use super accurate Planetary Theories (e.g. JPL DE405/LE405 or “Bureau des Longitudes” INPOP13C) and reach built-in accuracies [well] below the arc second level. Their sole limitations remain the unavoidable refraction uncertainties at low altitudes (up to 10°), as well as the irregularities of the Moon Limbs reaching the 1” level. Compared to the straightforward “one shot” Classical Methods, Modern successive approximations computations are huge and cannot be performed by hand at all.

    In other words, I am convinced that modern computation tools should rather use SEXTANT DISTANCES rather than CLEARED DISTANCES as benchmarks. Both are not equivalent at all because their variations can be extremely different, if not opposite under extreme cases (see Lunar #2). I am convinced that tackling Lunars the "modern" way is a much improved approach because the measured variables are the Sextants Distances, and not the geocentric distances. The latter are only a "medium" - no way then to do better - devised by our illustrious mathematician forebears who lacked our contemporary computing power. And, as a repeat, the geocentric distances (i.e. the "Cleared Distances") may not vary at all with time like the sextant distances from which they are derived. This is why focusing onto auxiliary variables which are not the real world quantities actually measured can be quite misleading.

    Hence my suggestion for improving your on-line Calculator, Frank, through implementing accurate and meaningful information about the expected accuracy of the Lunars we are computing on your site.

    I am aware that the ideas here-above might be a stone in the garden of some of you. But I am convinced that paying all due attention to " the “Longitude change / Sextant Distance change ratio” concept and its practical importance " is a key factor to better understand the accuracy which can be expected from Lunars. Such subjects cannot be adequately addressed with the sole use of the Classical Methods.

    I consider this post as one important contribution to NavList, if not my most important one. Maybe it has been addressed here at earlier times, in which case be so kind as to disregard all. Except if this "revamped" post raises attention - which until now has not been up to my former expectations, and in which case I will keep debating here - I will probably stop contributions on NavList because a number of subjects remain of less importance to me nowadays, and also because I lack finding here truly innovative subjects, although there could be many, such as the improvement of the CCD Cameras Lunars.

    Like all ideas, the ideas here-above are here to be discussed, and if necessary beaten down in order to get defeated. This is the name of the game here. I currently consider them as sufficiently strong to withstand a number of critics, and - again - if proved to be totally off-track I will happily change my mind because - as we all know - the most important remains "what is right" rather than "who is right ?".

    My "intended retirement" does not preclude all usual private contacts with my good "number crunching" friends, who can recognise themselves here.

    That's about all !

    Again ... ideas are meant to be debated, fought and even defeated.

    And last but not least, my heartiest congratulations to you all, and first of all to you Frank for so brilliantly "running" (I know, you HATE this word ...) NavList after starting it from scractch.

    Farewell to all under fair winds and following seas.

    Antoine M. "Kermit" Couëtte



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