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Thanks Frank,

Leave it to George Huxtable to coin words that seem almost off topic and more suited for the Freudian couch. "Parallactic Retardation" could easily be the freezing of the mind or a particularly bad case of stage fright ;-)

Greg Rudzinski

[NavList] Re: Recovering Time by Time Sight
From: Frank Reed
Date: 18 Dec 2012 16:12
Greg, you wrote:
"The longitudes differed by 28.3' which was the exact number listed as the ddGHA for the Moon. This ddGHA was from an online almanac not the Nautical Almanac. At Frank-what is this ddGHA number? 28.3' works out to .008' per second of time which means recovering time to better than 30 seconds would be tough."

This almanac author's ddGHA is equivalent to dSHA. Put it another way, if you knock off 15 degrees per hour from the GHA of all of the bodies listed, and then compare what's left, you'll see that the remainder changes at the rate given by ddGHA in the table. The Moon moves relative to the background of the celestial sphere at about 30' of arc per hour along the ecliptic. If it's close to perigee, it moves faster. Towards apogee, it moves slower --"doubly so" because it's moving physically slower thanks to Kepler's Second Law, and also slower in angular terms because it's farther away. In addition, since the Moon's orbit is tilted between 18 and 28 degrees relative to the Earth's equator, some of this speed along the ecliptic does not register fully as a change in SHA; some of it translates to a change in Declination.

The rate of change per second in the Moon's position that you quote is almost identical to the rate which I usually suggest folks memorize: 12 seconds for a tenth of a minute of arc (a useful number as a lower limit since few navigators expect to do better than that even under ideal conditions with numerous sights averaged). That's the best resolution of time that you can expect from any observation of the Moon's position relative to the celestial sphere. Bad geometry can make this much worse. If we do a traditional lunar, we measure the angle between the Moon and some star. That star should be more or less along the ecliptic directly ahead of or directly behind the Moon on its path through the sky. Then the measured distance will change at about that rate: 0.1' in 12 seconds (*see PS). If instead the star is off to the side, the distance will change more slowly. There's a wide region of the sky ahead of or behind the Moon that's acceptable. Forty-five degrees out of line is not a problem.

With altitudes of the Moon, in order to detect these changes in the Moon's SHA, we need to make sure that the Moon's motion is nearly vertical away or towards the horizon. Generally this condition is met when the Moon's horns are more or less horizontal or at least within 45 degrees of horizontal. In the tropics, this is a common occurrence. It's not rare in mid-latitudes either. The big catch with measuring these altitudes as compared with "ordinary" lunars is that altitudes --all altitudes-- are less exact than many other measurable angles because of the uncertainty in the dip. The weather affects the terrestrial refraction so the horizon can shift up or down in unpredictable ways. It's just a fraction of a minute of arc, but obviously that matters much more with this sort of sight. A good portion of this uncertainty can be eliminated by measuring the altitude of the other body nearly simultaneously with the altitude of the Moon on the same side of the sky. Or a very large number of sights could be taken (again nearly simultaneously... so ok, you get yourself some grad students) and the dip could be treated as a systematic error to be eliminated by minimizing the residual error.

Historically this lunar time sight cousin of lunars never caught on. The mathematicians found it inelegant or at least uninteresting, and practical navigators were apparently never persuaded by its advantages. The biggest advantage, of course, is that you don't have to learn much of anything new.

Any attempt to determine GMT by the Moon's motion, whether traditional lunars or these lunar time sights (or equivalent LOPs) has to face that daunting figure of 0.1' being equivalent to 12 seconds of time. You have to work all the calculations at a more detailed level than in standard navigation. And you have to pick up all the little corrections like the augmentation of the Moon's semi-diameter (the Moon is SMALLEST when it's closest to the horizon, contrary to the perceptual illusion). And you have to make sure your sextant is properly adjusted to the finest level to eliminate any errors as large as a tenth of a minute of arc. Many of the practical tricks as well as practical difficulties that apply to traditional lunars also apply to lunar time sights.

-FER
PS: *The Moon moves about 0.1' in 12 seconds relative to a star directly ahead or behind along the ecliptic when observed geocentrically. But we can't do that. Parallax due to our observing location 4000 miles from the Earth's center changes those rates. Even if the Moon were fixed in space, its position relative to stars would shift by nearly one degree as it travels from the horizon to the meridian (which it does in six hours or so, implying an average rate of about 0.1' in 36 seconds) due to that parallax. Hence the apparent rate of change can be somewhat higher or lower. Some of you may remember the phrase "parallactic retardation" which George Huxtable coined way back in January of 2004 to describe this. He later regretted the whole thing after Jan Kalivoda carefully explained to him that this was part of the clearing process. But unfortunately the baby was thrown out with the bath water, and there's an important point here which is still worth understanding. It might be worth getting into it again...

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