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    Re: Persistence and demise of Lunars
    From: Frank Reed
    Date: 2017 Dec 14, 18:37 -0800

    Bruce Cutting, you wrote:
    "I've seen comments about lunar distance tables. I'm wondering if any tables (other than the standard almanac) are needed."

    No. No other tables are necessary (though they're convenient). The tabulated lunar distances which were included in the almanacs into the early 20th century --already over 50 years after they had become obsolete at sea-- can be re-calculated without much trouble. It's just the angular distance between the Moon's center and the other body's center. Of course by angular distance we mean great circle distance, and we know how to calculate a great circle distance. So just get the GHAs of the two bodies and think of those as the longitudes of two cities on the Earth's surface, and get the Declinations and think of those as the latitudes of those two cities. Then apply your favorite procedure for great circle distance. Easy as that. Assuming you know your GMT to within five or ten minutes (surely never worse!), you calculate the expected distances this way for the hour before your guessed-at GMT and for the hour after. Then you observe the actual angular difference and compare by simple, linear interpolation. Imagining a lucky case with "clean" numbers, if we calculate the Moon-Sun distance is 75.000° at 1500 GMT and 75.500° at 1600 GMT and we observe a distance (after "clearing") of 75.100°... well, that's exactly 20% of the way from the first distance to the second so the time would be 20% of the way from the first time to the second. Thus the time is 1512 GMT. See? Just that easy!

    You added:
    "My understanding is that you need tow bodies (likely the moon and the sun, but that other bodies can be substituted for the sun). You need a fair guess at the observing latitude, date, and time, then use an iterative process to get actual La and Lo."

    No. In general there's no iterative process, and latitude doesn't really enter into it. You got the basic element correct though when you wrote, "1) measure the distance between moon and body (usually limb closest to the sun or selected body) 2) measure the altitude of both bodies 3)". That's correct. We use the altitudes of the bodies to correct the lunar distance. Both refraction and parallax are dependent primarily on the altitudes of those bodies. And the altitudes also tell us how much of each correction affects the lunar arc. Notice that these "two altitudes" do not give us a fix. Observing the altitudes can sometimes provide additional information, including those next steps in getting lat/lon, but that's not what they're for in lunars. The altitudes "corrrect" or "clear" the measured lunar distance.

    To puzzle this out for yourself, you'll learn an enormous amount by considering a case where the Moon and Sun are aligned on the same azimuth --one right above the other. Suppose, for example, I am in the tropics and I look in the eastern sky in the morning and see the moon low above the horizon and the Sun high up, right on the same azimuth. I have an assistant with a cheap plastic sextant who will shoot the altitudes of the two bodies, and I myself will measure the angle between the Sun and Moon with a fine, properly-adjusted Plath sextant. We approximately measure the altitude of the Moon (Upper Limb) as 20° 10' and the approximate altitude of the Sun (LL) as 75° 30'. In addition, I have with exceeding care and with the best accuracy I can manage measured the limb-to-limb distance between the Sun and Moon as 55° 17.3'. Also, assume 4' dip and zero index correction on both instruments. What, given these observations, would be the corrected lunar distance angle? You'll need one bit of almanac data to do the work, namely the Moon's HP. Let's suppose that's 58.0'. See if you can work it out. Or at least see if you can figure out the steps that would be required. It's a puzzle! This is called 'clearing the lunar distance'. The general case where the bodies are not aligned vertically, one right above the other, has been known to drive navigators batty. Yet it's just math, and it's math that was solved to more than sufficient accuracy over 200 years ago and implemented in a variety of different practical solutions. 

    You asked:
    "2) Where can I get more information"

    Right here. Ask questions... You'll be an expert in no time. :)

    And you concluded:
    "3) Is a sextant accurate to minutes and seconds good enough to get reasonable results?"

    You bet! Our modern sextants are a product of the lunars era. They were designed and improved specifically for the task of shooting lunars. In many respects, they're over-designed for the altitude sights that we normally use them for today. So, yes, you can use a good modern sextant to become a proper lunarian!

    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

       
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