NavList:

Martin, you wrote:
"Both average lunar and sun altitudes are the real altitudes taken with the sextant. When available, I always try to take the actual altitudes (an average them), because I after doing the lunars calculation, I use those same sights and times to do a regular sight reduction (LOP or cosine rule method) to check the position error (which in this case it was 1.2 nm)."

OK, but that wasn't the point I was trying to make. You quoted the altitude of the Moon's lower limb. There is no way that you could observe an accurate altitude of the Moon LL in daylight, especially when the Moon is more than half full. So what to do?? You should have taken a UL sight of the Moon. Or if you were using your bubble sextant, maybe you could have taken body-center altitudes. With normal Moon altitudes, we shoot the UL roughly 50% of the time. With lunars in daylight (where the other object is the Sun), we shoot the Upper Limb maybe as much as 80% of the time.

You also wrote:
"As you explained in the course, and I was able to confirm in the last lunars, a small variation in the sextant index error makes a significant difference in the cleared lunar distance, so I use the regular LOP sight reduction to confirm that the index error taken when calibrating the sextant makes sense. In my experience in doing regular sight reductions with the Mark II sextant the position error varies between 0.8 and 1.5 nm."

I have to say that using the Sun and Moon altitudes as a 'confirmation' of index error for lunars is largely useless. The system error of ordinary sextant altitudes, taken with a good open-sea horizon, is on the order of half a minute of arc. And a coastal horizon, especially with a nearly enclosed bay/estuary (like the River Plate) can be more like one or two minutes of arc easily, and sometimes more (because of unusual temperature variations in the air above bodies of water like that). Yes, you can confirm basic functionality of your sextant and detect some large-scale problem, but there's little merit in doing "LOP sight reduction". For lunars, you need to get your index error dead-on accurate, to the nearest tenth of a minute of arc, if possible, and shooting altitudes will not help with that task.

You continued:
"The average times are the correct ones, but the Mark II has a very small horizon mirror, so it is always a kind of difficult “to kiss” the sun and the moon, so it took me around 5 minutes to take four lunar distances."

In that case, you should have taken Sun and Moon altitudes after the lunar distances to accompany those taken before the lunar distances. That's the best way to synchronize them with the time of the (averaged) lunar distance. It's easy and accurate.

You wrote:
"As you said, the moon’s bight limb was clear enough to take lunar distances, but the altitude of the moon respect to the horizon was not a good one because the lower limb was too dark. That might have introduced a little error in the position calculation with the LOP method."

Maybe. Maybe not. But regardless, you should have just shot the Moon's Upper Limb for an altitude, as I noted above.

You wrote:
"I always use your app to see the lunar results and then I compare it with the spreadsheet I developed. This spreadsheet calculates both the cleared lunar distance and the true lunar distance, and that is another reason that I need to take the precise moon and sun altitudes with the sextant (and the corresponding times)."

You do not need precise moon and sun altitudes. They are not necessary in typical cases to better than a few minutes of arc accuracy, and in some popular cases, when the Moon is "in distance" (close to 90° from the Sun), the Moon's altitude (specifically the Moon) can be wrong by a degree or even more, and it produces no error in the results. The geometry is forgiving!

You listed some lessons from all of this:
"Sextant calibration and using the correct index error is critical in the lunar’s precision."

Absolutely. Yes! In common altitude sights, we don't worry about the tenths of a minute very much on the index error because we know that the system error (all the pieces of the process, put together) amounts to around one minute of arc, and a better index correction will only have a small impact on that. But with lunars, every tenth of a minute of arc error shows up in the results because the system error for lunars is much lower, around ten times smaller.

And:
"Always run a regular sight reduction using the moon and the second body (if using real altitudes imputs) to make sure the sextant is working properly."

Well, as I noted above, this could detect a gross error, but otherwise it's not much use.

Regarding your sextant, you wrote:
"The Mark II sextant reading marks are 0.5 separated, so I had to estimate what decimal to use."

This should not present any problem, and it is not specific to that model of sextant. It's easy enough to get the tenth of a minute of arc "by eyeball".

And also:
"The Mark II telescope is not very powerful and that combined with the small horizon mirror makes it not the most appropriate one for lunars."

The telescope is definitely a limitation. Magnification absolutely enhances the quality of lunars results, and it's more or less in simple proportion: five times greater magnification means five times better resolution of that final step of bringing the Moon's limb into contact with the other body. Corrected vision by eye has an expected resolution of about a minute of arc. Magnify by 5x and we can see details as small as about 0.2 minutes of arc. And so on...

But don't forget that there's no law that says we have to get some level of perfection from every sight. For a modern observer, the best benefit of shooting lunars is to see what you can really accomplish with a --specific sextant, as is, without lunars-specific enhancements. Have you ever tried shooting lunars with a Mk 3 plastic sextant (that's the one with no scope and no micrometer)?? Most navigators would say that you "cannot" shoot lunars with a basic sextant like that one --not ever! But of course you can. And when you do, you learn what the instrument (and you as an observer) are really capable of achieving.

Frank Reed