You are so far the most knowledgeable person on the subject that is at Subsim that I've had absolutely nobody to talk to on the subject. What is the time, date and location of your graphics. I don't think the average person can understand them and I think they deserve to. The scale is also too small to read the text.
Let me try from an astronomy program I use called
Carte du Ciel. I'm not going to be able to pick the same location on Earth, but I can pick one at about 35 degrees latitude. I'll have to download into my Linux installation and I'll do it tonight.
First let's set the observing location:
Now let's look at the sky in Carte du Ciel, whole sky view:
A couple of things of note. The altitude is the altitude of the center of the object, not the limb. The moon at zero altitude is half visible. Then look at the altitude at 29'58.5", essentially that's 30 minutes high. Since the moon is 30' wide that means that to the eye, the entire moon is visible with 15' of clear space below. You won't see that without a telescope, if you're lucky.
But look at that thing below the altitude. Nathaniel, you know what that is, but I'm explaining interesting stuff to others. The Geometric altitude is where the moon REALLY is. You see, our atmosphere acts like a lens, bending light that enters it from an angle. For objects on the horizon, and this thing qualifies, you can see that atmospheric lensing raises the moon from only 1 minute above the horizon (half visible) to 30 minutes above the horizon where you can see the entire Moon with half a moon diameter of black space below the moon! Rule of thumb: on the horizon all objects are raised by about half a degree.
And in the far corner of the sky sits the Sun. Its altitude is 1 degree 39' 10.3", but its REAL altitude is 1 degree 19' 13.4". Now the moon isn't perfectly full, but pretty close, and you can see that with the Sun 1 degree 39 minutes above the horizon (you can just see all if it IF you have a perfect horizon plus perfect sky) and the Moon half a degree in the sky (there is a quarter degree of sky under it, not really enough to see even with a telescope unless your viewing conditions are perfect) they are essentially rising and setting as a unit. Considering that every day the moon's rise time is 50 minutes earlier and we're only 3 minutes apart comparing rise time of sun to set time of the moon this is pretty close to an ideal situation. You can possibly measure that they are not EXACTLY 180 degrees apart, but I daresay that no instrument of a submarine or ship would establish that. Measuring positions of objects on the horizon is basically impossible anyway.
And that's why you mentioned shooting noon positions. That's much more accurate. Straight up, you don't have to worry about atmospheric refraction. Since you are looking through the minimum thickness of atmosphere, seeing conditions affect you the least they possibly can for that particular weather condition. BUT the time of culmination, when the Sun is highest, depends on your longitude and YOU DON'T KNOW THAT. So you don't know exactly when to look to find the time of local noon. Of course navigators have sneaky and effective ways to deal with that uncertainty;
Nathaniel, take it away! How about explaining how to do a noon sight and how to use that information to develop your longitude? Latitude is a piece of cake. Just measure the altitude of Polaris. If you're being fussy you can use a polar alignment scope to correct for the offset of Polaris from the actual pole, but that's less than a degree. If you're south of the equator then the bet is off!
Did you know: the rate of continental drift in the Atlantic Basin, the rate the moon is increasing its distance from Earth and the rate your fingernails grow are all just about exactly the same? Coincidence? Or conspiracy?