NavList:

Jim H, you wrote:
"I know this has been covered over the years to a greater or lessor extent"

Please [and this is directed to everyone reading this message] never let that stop you or discourage you in any way from bringing up a topic for discussion! 

You asked:
"what is the criteria used to determine if a calculated lunar distance is usable beyond the obvious ones such as visible, and in distance?"

Historically, in almanacs that included lunar distance tables, there were nine lunars stars plus the Sun. Beginning in the 1820s and 1834 in the standard British "Nautical Almanac & Astronomical Ephemeris", the bright planets were also included when appropriate. So that's the first condition: it has to be on the list.

Next up, the Moon had to be at least one day away from the Sun. I don't recall if almanac editors had any absolute rules on this one. And the distances had to be in sextant range so they usually topped out at 120° or maybe a little higher. At the low end of the distances, the problem was non-linearity in the change of the distance with time. Given that the distances were provided once every three hours, this implied that distances less than about 15° were not useful.

The tabulated lunar distances were used historically for determining Greenwich time. Before 1834 the tables were given for every three hours of Greenwich Apparent Time. After that, they were indexed by Greenwich Mean Time. Since the goal was to determine time, it was also required that the distances had to have a large enough rate of change. If you imagine a bright star, like Altair (which was one of the official nine stars) aligned right along the line through the horns of the Moon, you can see that there would be a problem. The Moon's motion among the stars is nearly perpendicular to the line through the Moon's horns. So if Altair is perpendicular to that motion, the angular distance to it would change very slowly. It could not be used under those circumstances to determine time with any accuracy. If you examine the published lunar tables, the rates of change seem to imply limits where the star or planet would have to be in the forward or rear 90° wedge relative to the ecliptic (near enough to the Moon's direction of motion). That is, a ray drawn from the Moon to the star could be up to 45° off the ecliptic, above or below, and it would still be included. Using stars well of the axis of the Moon's motion would imply a roughly 30% reduction in the accuracy of the determination of time. So if a navigator could determine Greenwich time within +/-30 seconds using stars directly aligned with the Moon's motion, the time accuracy would be about +/-39 seconds for stars as much as 45° off-axis.

In the modern world, all of these conditions can be relaxed under many circumstances. First, we can easily calculate predicted lunar distances for any star. My online Lunar Distance Almanac allows you to select from various lists. Second, since we can tabulate lunar distances at shorter time intervals, we don't necessarily need a low-end cutoff at 15° (we can interpolate with hourly tables). And, though we're still limited by sextant range, we can easily go beyond 120°. Finally, lunar distances today are more likely to be used to test the sextant and observer, and there's no requirement to get Greenwich time from the result. That means we can shoot stars in any angular position relative to the Moon's motion.

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA