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    Re: Basic questions about Lunars
    From: Frank Reed
    Date: 2013 Jan 23, 14:05 -0800

    Norm, you wrote regarding the minimum in the rate of change of Jupiter's angular distance from the Moon:
    "Is this right?"

    Of course! :) We did discuss this in the past couple of days, and you may want to look again at a couple of earlier messages. But there are no miracles here. The Moon moves nearly along the ecliptic. If the other object from which we're measuring a "lunar distance" is off to one side or the other, then the rate of change of the angle between them will drop to zero at some point and therefore our ability to measure Greenwich time by observing this angle becomes quite inaccurate for a while. Of course, it's still a lunar observation which you can treat as either a practice lunar, or a test of your sextant and skills, or a lunar used for a position fix (see my comments in a recent message about Apollo 8 and also in many earlier messages over the years).

    Historically, this issue of slowly changing lunar distances was never a problem. No navigator ever had to decide because the editors of the Nautical Almanac (and its cousins in other cultures) already made the correct choices. There were nine traditional "lunars stars": Spica, Antares, Altair, Fomalhaut, Markab, Hamal, Aldebaran, Pollux, Regulus (for a very few years beta Capricorni was also listed as the tenth "lunars star"). These are mostly bright stars close to the ecliptic so the Moon's motion is more or less directly towards or away from the stars. The major exceptions are Altair and Markab (alpha Pegasi). The rate of change in distance to those stars would be too slow in cases where the Moon was relatively close to them in the sky but much farther than the cases of the other 7 stars. So why didn't they just choose better stars? Get out any star map, and you will see the problem. There aren't any better stars. For those two stars, the almanacs listed their distances only when they were relatively far away from the Moon so that the lunar distance was still changing rapidly enough to be useful.

    For a modern navigation enthusiast, since the lunar distance tables may not be available, you may want a standard to decide whether a given body is appropriate for the determination of GMT/UT by lunars. To do this, draw a line across the sky through the Moon's center perpendicular to the line through the Moon's horns (nearly the same as a line along the Moon's equator, and if you can't see the "horns" of the Moon because it's nearly full, just use the Moon's equator). The Moon moves across the celestial sphere (that is, relative to the background stars) nearly along this line. This line should be nearly parallel to the ecliptic and separated from the ecliptic by at most 5.2 degrees. Now draw a second line from the Moon's center to the star or planet you're thinking of using (these "lines across the sky", by the way, are technically great circle arcs). Look at the angle between this ray and that first line you drew. If that angle is less than 45 degrees, you're probably OK. The rate of change in the distance for angles at 45 degrees will be reduced by only about 30%. This means that we will be able to discriminate GMT at a resolution of about 17 seconds of time for every tenth of a minute of arc error in the distance instead of the average 12 seconds of time. That appears to be close to the standard that was used historically when deciding whether to list a star off the Moon's track in the lunar distance tables.

    And you wrote:
    "Also, could you point me to the tables that would be used, assuming I get my sextant working (highly possible)?"

    They're in Bowditch and Norie. You have to decide what method to use. It doesn't matter much. Just pick one that was popular. If you want a recommendation, I would suggest any of the first three methods in Bowditch for any date from 1802-1880 and more specifically the second method as listed from 1837. You can find all of these in the NavList "historical navigation books online" index located here: http://www.fer3.com/arc/navbooks2.html. But take your time on this... There's no need to dive into a historical, paper method right off the bat.

    To clear a lunar in the modern world, you should just try some observations and check your results with my online clearing tool, which is far easier than any of the historical methods and also somewhat easier than most of the other available modern equivalents. It's located here:
    specifically here:
    It does all the calculations for you including the ephemeris data for the Moon and the other body, accurate to one second of arc. Just shoot some lunars recording the GMT as you go. Then enter your latitude, longitude, your instrument's index correction (IC), and also weather conditions if they're unusual. Height of eye is needed only if you observe your altitudes separately, which is not required but would have been done historically at sea. The online calculator will tell you how far off you are from a correct observation in minutes of arc and will also give you an equivalent longitude error (strictly for teaching purposes: this is "equivalent longitude error" for a typical observation, not the specific observation in question).

    Oh by the way, since we were discussing your sextant's telescopes, don't forget that you can make "unit magnification" observations with your sextant. In other words, take the scope out and use your unaided vision (corrected by eyeglasses or contacts, of course). Sight right along the frame where the scope would normally be fixed. There's some collimation error if you don't sight right along the frame, but there's a way of dealing with that, too, if you're interested. Naturally, you will be limited by the normal resolution of the human eye which is about one minute of arc. But that's fine when you're first trying things out.

    You should also try measuring the diameter of the Sun as I described in a few posts earlier this month. Although most navigators and navigation enthusiasts are under the impression that this is "merely" a method for measuring index correction, they're quite wrong. It's a real angular measurement which is comparable in many respects to a short angle lunar and which has the huge additional advantage of being available for practice every clear day. And since it changes so slowly, taking weeks to change by a single tenth of a minute of arc, it's easy to compare one's results with the true angular diameter of the Sun.


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