NavList:

Regarding Brian W.'s trial method for using a lunar altitude for a GMT test, I wrote:
"But have you actually accomplished anything here? I think you'll discover if you look at it again that you have talked yourself into something that feels like a correction to GMT, but it isn't anything of the sort. [I've got a folder full of things like that myself!]"

I had hoped by mentioning that I have a 'folder full of such things' I would make it clear that experimentation is a good thing! We just have to be prepared to recognize that some experiments don't work. They get filed away. Also, it's important to emphasize that the issue with Brian's specific proposed method does not in any way represent a flaw in the concept of getting GMT by lunar altitudes. The problem with Brian's method, as proposed, is closely related to an issue that most people encounter when they first learn about lunars.

When we first discover the idea of lunars, we're reminded that the Moon shifts its position at a rate of about half a degree per hour of time (which is half a minute of arc per minute of time, which is 0.1' in 12 seconds of time --on average!). But wait a minute, we know that the Sun shifts its position at a rate of 15° per hour. So why would we turn to the Moon?! We use the Moon because that half a degree per hour motion is relative to the "celestial sphere" or the "stars themselves". The 15° motion of the Sun is its usual "diurnal" motion, its rate of change of GHA, due to the Earth's rotation, and the Moon participates in that, too. When we see both the Sun and the Moon in the sky at the same time (let's make it a waning moon), we can watch the Sun and Moon cross the sky at nearly the same rate. The Sun moves west at 15° of hour angle per hour. The Moon moves west at about 14.5° of hour angle per hour. It's the small difference that allows us to determine GMT. They share the diurnal motion, resulting in nearly the same rate of change of GHA. It's the changing "SHA" (in modern terms) of the Moon which allows us to distinguish GMT with careful observations.

There's an easy way to apply something close to Brian's method as a first approximation. Take the east-west separation in minutes of longitude between the Moon LOP and another "longitude" LOP (or fix from crossing LOPs) that you trust. A fair approximation would apply the average rate of shift in the Moon's SHA to that LOP. That's 0.1' in 12 seconds. So if the point on your Moon LOP is ten minutes of longitude west of your "fix", then you would adjust your GMT by 1200 seconds --as a first approximation. Yes, that's 20 minutes of time! Now, of course, you're not going to go monkeying with GMT at that scale unless you have really good cause. But such cases can arise. For example, suppose you haven't had a GMT check in days, maybe because you've been in a storm (*). Maybe your only watch got dunked, and you've had to rinse it out and replace the battery. In the meantime you kept time by counting sheep... Two hours later, when you've got it running again, your watch could be wrong by twenty minutes. A Moon LOP could help reduce that error. I wouldn't trust a single lunar altitude for this. But if three or four tests in a row all showed the same gap between a lunar LOP and other LOPs, then yes. That's a solution. Notice that a more accurate revision of GMT could be achieved by replotting all the LOPs with an adjusted GMT. Then by trial and error two or three times, you could nail it down. But that probably wouldn't add much to an initial guess given the uncertainties of the sea horizon in the first place.

I wrote previously:
"And as another reminder, this trick of determining GMT/UT by a lunar line of position (or more generally a lunar altitude compared with a star or Sun altitude) is almost always inferior to a standard lunar. Standard lunars are more accurate intrinsically, and standard lunars almost always involve less math work. Note the two "almost always" modifiers in that last sentence! The exceptions can be interesting. :)"

Seek ye only perfection in thy lunarian methodologies! That sometimes seems to be the precept that lunarian curmudgeons have operated under. :) But time by lunar altitude, even though it is less perfect than proper lunars, has value. We just need to know what that value is, and we need to know which lunar altitude sights and sets of sights can maximize that value. Those exceptional cases, as I say, can be interesting, and we can do things to improve our results. We've discussed recently that we can reduce uncertainty in refraction by taking both sights from the same horizon (consider the scenario "Vertical Lunar I" that I posted earlier... the Sun and Moon are on opposite azimuths but the Sun is high enough for a back sight!). Also, we should expect good results when the "horns" of the Moon are more or less horizontal and not at all when the Moon is "standing up-right". But we should never expect the same quality from GMT by lunar altitude that we get from GMT by lunar distances. In the general case, lunar altitudes are inferior. In a specific circumstance, perfection is an illusion, and we should not ignore a good tool.

Frank Reed
* Related to this idea of losing twenty minutes in a storm, Letcher in his "Self-Contained Celestial..." has a nice little section on recovering the date. Here he supposes that we've been in a storm long enough to lose track of whether today is Monday or Tuesday. That could happen, sailing single-handed in the middle of the ocean. What then? Eventually you'll get the date by radio, but in the meantime, you can do a very crude lunar distance, or you can simply plot the Moon's position on successive dates. If you see the Moon in evening twilight a few degrees from Antares, you would know the GMT to the nearest hour (same as the GMT in evening twilight before the storm began, nearly enough), so you pull out the SHA (a little calculation needed with the standard almanac tables) and Dec of the Moon, and you plot them on a star chart (the one in the standard N.A. is not terrible). One will show the Moon a few degrees from Antares just as you have observed. Date determined!