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    Re: Lunars: Point of contact between two celestial bodies
    From: Frank Reed
    Date: 2023 May 23, 10:10 -0700


    I enjoyed reading your thoughts on the point of contact between the Sun and Moon. As I have written to you previously (within the past couple of weeks), I agree completely that Sun-Moon lunars produce the best results, and I agree that it has something to do with the visual process. Human vision is still a bit of a mystery, and it is possible that this is a hyper-acuity task. There's a good Wikipedia article on this topic here: https://en.wikipedia.org/wiki/Hyperacuity.

    And for anyone else reading along, an earlier name for this "hyper-acuity" phenomenon was "vernier acuity", and yes, they were talking about the improbable accuracy of instruments with long vernier scales like 19th century sextants. How does it work?? We don't really know. It doesn't quite make sense in terms of the optics of the eye, but human vision is much more complicated than a simple biological camera.

    It's also worth saying that some people have much better visual acuity than others, and I think there's evidence in your descriptions, Modris, that you might be one of those people! In a way, you were born into the wrong century. A hundred years ago or more you might have been a prized observer in a major observatory measuring binary star separations and position angles. That was a task that demanded observers with refined vision and observing skills. Alas, that sort of work was handed off to photographic plates and measuring engines long ago, and of course today even amateur astronomers do exquisite measurmement work via apps and other code.

    Of course we have to maintain a degree of skepticism. Well, we don't "have to" :) ... This isn't a scientific journal! But if I treat your thoughts with respect, then respect includes skepticism, so I must :). 

    Some of what you describe may be confirmation bias. Since I'm sure this concerns you, too, I wonder if you have any tricks that you use to avoid this? You discussed repeatability of sights where you get very small, repeatable errors within a small set of lunar observations taken in sequence. Do you do anything between individual sights to "randomize" the process? Sometimes, to test myself, when I shoot a run of four or more lunars, I will "spin" the micrometer after each individual sight to make sure that I am not biased by the "feel" of making the same small turn after each sight. An adjustment of the micrometer by a tenth of a minute of arc is the tiniest tweak that I can imagine. I encourage anyone else reading along to try adjusting your sextant's micrometer by a tenth of a minute of arc. It's a motion you can barely feel with your fingers... Since a sextant micrometer is completely analogous to a seconds hand on a wristwatch, imagine trying to adjust a seconds hand by a tenth of a second. That small "bump" is identical to a tenth of a minute of arc on a sextant micrometer.

    Your description of that overlap "lens" was really good. From a mathematical perspective, this is closely related to that little sketch I included in a recent post describing the overlap "sector". If we specify a depth of overlap in seconds of arc, then we can calculate the angular width of the circle sector measured from the center of the Moon. For small angles it's proportional to the square root of the seconds of arc of overlap depth. The width of your "lens" is the same thing. As the overlap diminishes linearly with time or linearly with a steady, slow rotation of the micrometer, that overlap "lens" decreases in width at first slowly and then quite rapidly. That may conceivably provide a visual clue that helps to make Sun-Moon lunars more accurate. I'm already contemplating some experimental observations for later this week as the Moon comes into distance (First Quarter on Saturday!).

    No matter how much accuracy you're able to get in your observations, it doesn't bypass the fundamental limits of the process itself. I've already warned you about the lunar limb "mountains" problem, which is the major limiting issue under most lunar distance geometries. You might also want to contemplate other limiting phenomena, like frequency "dispersion" of light. Refraction depends on wavelength. The light of the Sun (and the nearly equivalent spectrum of moonlight since it's just reflected sunlight) is basically white, with light all across the full width of the visual spectrum. When the Sun and Moon are moderately low in the sky, they display a subtle, fuzzy "fringe" all along the upper and lower limbs. Stars and planets become colorful vertical streaks, like tiny "French flags". These are essentially multiple overlapping images of each body at different wavelengths in the visual spectrum displaced up or down by a few seconds of arc. At the very lowest altitudes, this can even be a problem for "ordinary" celestial navigation. There's no easy way around this except to eliminate all lunars when either body is below some limiting altitude (...15°? ...30°? a limit to be determined by other analysis which will necessarily have an arbitrary element because we're talking about a "fuzzy" edge).

    Frank Reed

    PS: Speaking of refraction, what is the "correct" and "official" refraction of a star's altitude when the star's altitude is in the range from 10-20°? If you open the Nautical Almanac, you have two choices. You can consult the tabulated values on the inside front cover. Those values are nominally provided to a tenth a minute of arc, but because it's a critical table, you can read out to a precision of 0.05'. Meanwhile, in the computation section in the back, an equation lets you calculate refraction values. If you do so, you'll find that the computed values are higher by roughly 0.1 minutes of arc. Which would you like to use? For ordinary celestial altitudes, the difference is inconsequential. But for lunars?

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