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    Re: What is the Longest Lunar Possible?
    From: Brad Morris
    Date: 2013 Jan 21, 14:59 -0500

    Hi Frank

    I used your online lunar predictor to discover the following Sun - Moon distances for Long Island.  The filter was to reject anything less than 150 Deg.

    24 Jan 2013      153+ Deg
    23 Feb 2013     156+ Deg
    25 Mar 2013    160+ Deg
    23 Apr 2013     154+ Deg
    26 May 2013    162+ Deg
    24 Jun 2013      165+ Deg
    20 Jul 2013       154+ Deg
    24 Jul 2013       155+ Deg
    22 Aug 2013     160+ Deg
    21 Sep 2013     154+ Deg
    20 Oct 2013      161+ Deg

    With any luck, I will get one of these with the reflecting circle. 

    However, it appears as though the horizon is the limiting factor. Hence the question about being above the (ant)arctic circle to eliminate the limiting horizon.  If you properly positioned yourself so you were standing perpendicular to the ecliptic, would you then see both the sun and moon with the moon full?  I think the answer is yes.  Place the sun and moon at the greatest declination towards your position.  That should cause them to be at or above your horizon!  So in this rare instance, I do think latitude does matter!  Your thoughts on this particular point would be appreciated!

    The plane of the reflecting circle would then, of course, be nearly parallel to the ecliptic AND the horizon.  Why nearly?  Because you would be away from the ecliptic by the radius of the earth, with the sun and moon presumably near to the ecliptic at great distance!

    Regards
    Brad



    On Jan 21, 2013 11:38 AM, "Frank Reed" <FrankReed{at}historicalatlas.com> wrote:
    >
    > ________________________________
    >
    > Brad, you wrote:
    > "Is there a place on earth where we could observe a lunar distance of ~180 degrees? Perhaps in the polar regions, where the sun never sets but skims the horizon and the full moon simultaneously visible to the observer?"
    >
    > Wait. Don't buy your tickets for the Arctic yet! How about any place on Earth, a day before Full Moon, at sunset? Maybe January 25 on Long Island at 4:30pm? :-) Right? If you want to see the Sun and Moon separated by nearly 180 degrees, just wait for sunset when the Moon is nearly full. The altitudes will be low so you have to worry about refraction, but you can see them separated by nearly 180 degrees. If the (corrected) angle is greater than about 179.5 degrees, you'll see a lunar eclipse with the Sun and Moon both above the horizon (a seemingly impossible bit of geometry which attracted the attention of a classical Greek philosopher, which we know today is possible because refraction lifts both bodies above the horizon). And of course, if you don't mind using a body besides the Sun, you could try this on any other day of the month when the Moon is up and a very bright star or planet is on the opposite horizon. Obviously that would take some careful planning or really good luck. Waiting for the day before Full Moon at sunset, or the day after at sunrise, seems like an easier approach.
    >
    > You asked:
    >
    > "Would the standard clearing methods work for this lunar?"
    >
    > Up to a point. Traditional tables naturally assumed that no one would shoot lunars above 120 degrees. Some had specialized correction tables that topped out at or near that limit. And of course the predicted tables in the Nautical Almanac and all other equivalents never included distances much above 120 degrees, so you would have the labor of working those out from RA and Dec of the two bodies. Otherwise angles near 180 degrees are "just as bad" as angles near zero and for the same reasons that I described previously. But angles as low as, say, 25 degrees and up to 155 degrees (180 - 25) present no fundamental difficulties except that the sextant doesn't measure angles that large. Your reflecting circle might do better.
    >
    > You asked:
    >
    > "Frank, you warn of errors when the distance is short, but how about when very long? Would your calculator work?"
    >
    > It should work at all angles.
    >
    > Brad, you wrote:
    > "Lunarians may be familiar with Cook's lunar to 155 degrees. I still don't understand how he measured this, given his equipment. He didn't have a circle of reflection, so how did he do it?"
    >
    > They had a special attachment for shooting back sights (I can't remember the maker's name off the top of my head, but it was believed to be an innovative device). Remember, this was a voyage of experiment as well as exploration. They "tried this out" but after the voyage both the attachment and the associated experiments disappear into history. We can either conclude that the experiments were deemed unsatisfactory by the observers who conducted them, or that Maskelyne was unimpressed with the results. In any case, the lunar distance tables were never extended to higher angles, the attachment never made it to market, and such very long angle lunars have remained a footnote in the history of navigation ever since.
    >
    > You asked:
    >
    > "What is the longest lunar distance successfully measured and cleared in the log books? Is there any recorded measurement at, say, 160 degrees or more?"
    >
    > Apart from the Cook lunars which you looked into, in more "normal" logbooks, I have seen worked lunars with distances up to 120 degrees and as low as about 40 degrees. But there was a strong tendency to prefer lunars in the range of roughly 70 to 100 degrees. I'll answer Sean's post for more details on that.
    >
    > There is an interesting observational problem with long distance lunars. How do you orient the sextant? This is siimilar to the problem of finding the correct spot on the horizon for an altitude of the Sun when it's nearly 90 degrees high. You have to rotate the instrument through 45 degrees or more in orientation, keeping both objects in view until you find the minimum. It's not sensitive to a modest error in orientation (e.g. 1 degree), but this is a novel manual activity with the sextant that would be difficult to learn given the rareness of such sights.
    >
    > There's one case where you can measure the Sun-Moon distance near 180 degrees without a sextant. The radius of the Earth's shadow at the Moon's distance is about 56% of the Moon's HP. So if you record the time when the Moon first enters the Earth's umbra (not possible to better than about one minute of time), you have something like a lunar observation at that point (no clearing necessary!). At that instant the true distance from the Sun's center to the Moon's far limb is 180-0.56*HP, if I am adding this up right. If the Moon goes into total eclipse, entirely within the Earth's umbra, at the instant when the last bright part disappears, it's the same angle, 180-0.56*HP, from the Sun's center to the Moon's NEAR limb. By the way, I would NOT refer to such observations as "lunars". Timing a lunar eclipse is in the same general family of phenomena, but, just keeping the terminology straight, it's not a lunar.
    >
    > -FER
    >
    >
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