NavList:

David Pike, you wrote:
"In struggling with whether Regulus was good for lunars at 06.38UT on 4 March 1942, I’d forgotten one thing and failed to notice another.  I’d forgotten that Regulus is very close to the Ecliptic and failed to notice that at the date and time selected the Ecliptic was close to vertical.  It’s also very bright, so not withstanding refraction, it would have been OK for a lunar."

Struggling or not, it sounds like you worked out some of the key details just right. Yes, as you noticed, Regulus is very close to the ecliptic which means it's great for the traditional historical use of lunars, finding GMT/UT by measuring the angle from Regulus to the Moon. The Moon can still, occasionally, be in a poor location relative to Regulus (picture the line through the horns of the Moon pointing right at Regulus just a few degrees directly above or below the Moon), but it's a rare geometry that spoils it, and mostly Regulus lunars will yield good values for GMT/UT.

The next part is just good luck on the day in question. Josh Carty apparently noticed this after setting up that Op K story [I'm assuming so... Josh??]. Early on that night in that latitude (this is important, too), the ecliptic was essentially vertical, which also implies that this was a "vertical lunar". And this is a nice opportunity to think through the complete process of a lunar with conveniently simplified geometry. Vertical lunars can be very simple.

In this scenario, we had the nearly Full Moon (one day past) rising close to East with Regulus on almost exactly the same azimuth above it. Josh's story also gave us a GMT which we could safely assume is accurate to some seconds but not the date. As you noted in an earlier post, you did determine the date from the constraint that it was "early" 1942 and then looking at the very approximate Moon-Regulus angular distances for dates also near Full Moon. Right?

Josh Carty's setup:
"At 06:37, the altitude of the Moon (LL) is just about 8°10'. The horizon beneath it is nicely illuminated. And the star Regulus is directly above the Moon, nearly on the same azimuth, so far as I can judge. I measure from the Moon's Lower Limb to Regulus and get 31° 07.0'. My watch says 06:38:05 GMT."

We need to do two calculations here. We need the geocentric lunar distances for the GMT before and after the lunar observation. Historically these were three hours apart, but we're free to use much closer limits in a semi-modern example. For example, get the GHA and Dec for the Moon and Regulus at 06:35:00 and 06:40:00 on 4 March 1942 from an almanac or modern source. The geocentric distance between the two is just the standard great circle distance (GHA is longitude, Dec is latitude, as always!). These will be geocentric angles from the Moon's center to the star.

Next we need a comparable quantity derived from the observed lunar distance: the observation corrected --or "cleared" as they used to say-- to make it geocentric.

Since the scenario suggested an angle from the Moon's Lower Limb, we have to subtract the Moon's SD first. So from the original 31° 07.0' subtract the Moon's SD specific to that date, GMT [and also it should usually be slightly adjusted by the Moon's augmentation in SD but that's nearly zero in this specific example].

Next we need to get rid of the effect on the Moon's parallax and also the refraction for both objects. How much are those? And do we add or subtract? Refraction lifts both objects, but the Moon more so (since it's lower in the sky). So the observed distance has been somewhat shortened by refraction. This is easily calculated. Fix that by adding on the net (combined) refraction. Then for the parallax, the Moon is lower than its geocentric position thanks to (topocentric!) parallax, making the distance between the two bodies considerably longer than it should be. That's easy to calculate to, so we fix that, too. We subtract that parallax correction. Parallax and refraction removed.

Now just compare the "cleared" distance with the almanac-based geocentric angles. This observed lunar angle, now corrected for parallax and refraction, should fall about 60% of the way from the LD we calculated at 06:35 to that at 06:40. Does it?? Work out the actual fraction... It should be darn close, assuming Josh Carty's are good. :)

And just like that you've got GMT from a lunar. Easy! This case is especially easy because it was a vertical lunar. Such cases are fairly common in the tropics.

Frank Reed