A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2013 Jan 21, 08:36 -0800
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.
"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.
"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.
"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.
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