[Sean C]

Originally Posted by Rockin Robbins

(I'm driving myself crazy here trying to visualize this stuff.) [...]

And of course, your math verifies that but is meaningless for most humans. Even you, comfortable with the math, haven't made the connection to reality that is vital to understanding whether it is true or false and vital to actually understanding what the numbers mean. Numbers have no meaning in and of themselves. They must be connected to reality.

First of all, I'd like to say that I'm no mathematician. Math was actually my worst subject in school and I absolutely hated it. However, if you're like me and find you have a passion for celestial navigation and devote years to studying it, you will learn to do the spherical trig because that's the heart of celnav.* Whether or not the equations mean anything to you personally is actually irrelevant. The equations I quote are literally the science behind the planning and practice of celnav.

Having said that...I totally understand what you're saying about visualization, because that's also how I understand and integrate new knowledge. So, with that in mind, I have prepared a few pictures to help illustrate why the Moon's phase is only tangentially related to rise or set times and even then only under certain circumstances. (Apologies for only being able to link to the pictures. Apparently, I haven't yet earned the privilege of attaching my own pics in-line in a post.)

Let's take a look at the case you cited as a "check":

Originally Posted by Rockin Robbins

Just as a check, what time MUST the full moon rise? There is only one time it can rise.

Many times, it is useful to look at an extreme example of a situation to understand the mechanics behind it. So, let's assume we are almost at the North Pole...our latitude is 89°59'59"N. Only one arc second away from the pole itself. Our longitude is 0°00'00"E. We are on the Greenwich meridian and therefore our local time is exactly equal to UTC. The date is September 6th, 2017 and the time is 07:30 UTC. The Moon is full (as full as it will get at this time at 99.9% illumination). Now, what is the Moon's altitude? If you click on Fig. 1, you will see that it is at 8°54'21" below the horizon (represented by the green circle).

Next, we wait six hours until 13:03 UTC. Now what is the Moon's altitude? Fig. 2 shows that it is still 7°53'18" below the horizon. Another six hours later at 19:03 UTC and Fig. 3 shows that the Moon is still 6°50'38" below the horizon. So what time will it rise? Well, the bottom left corner of Fig. 3 gives away the fact that the Moon will not rise at all on this date, at this location. In fact it won't rise until two days later, on September 8th, at which point it won't set again until September 20th...another twelve days away.

Suppose our latitude was 45°00'00"N (still on the Greenwich meridian, back on September 6th). Now what time will the moon rise? Fig. 4 shows that it already rose at 18:22 UTC the previous day. And if we were almost at the South Pole...what then? Fig. 5 shows that the Moon never rose on this day. At this latitude and time it is "circumpolar", meaning it stays above the horizon all day.

So, "what time MUST the full moon rise?" The answer is: it depends. But, on what? ... If you answered "the observer's latitude", congratulations! You are correct...partially. Unlike the Sun, the Moon is revolving around the Earth as the Earth itself rotates. The speed of the Moon's revolution is great enough that, the farther away from Greenwich you are, the more the time of Moon rise/set changes from what is listed in the Nautical Almanac.

That is why there is a "Table for Interpolating Sunrise, Moonrise, Etc." included in the N.A. This table allows for the adjusting of sunrise/set times for latitude and Moon rise/set times for both latitude and longitude.Because these are two of the primary factors which govern what time the phenomena occur for a given observer.

As I said: I have spent years intensely studying celestial navigation. I'm not just speaking from some cursory understanding of the subject. I own several sextants and have taken hundreds of sights, including "lunars". I have even generated my own "Time Sight Logarithm Tables" which can be used to navigate the way sailors did back in the 19th century. You may have noticed that my forum nickname is actually the name of the author [or editor, more precisely] of one of the most famous American books on navigation at sea: Nathaniel Bowditch...author of The American Practical Navigator, otherwise known simply as Bowditch.

Anyway, I hope all of that was clear enough. And I hope to be able to help DaveR with his problem...although from my initial calculations, it seems that SH might actually have some inaccuracies. I'll need to investigate further and get the answers to my questions to really know. We'll see.

BTW, for some reason I can't see the picture you posted. All I get is a rectangle containing a circle with a horizontal line through it. (?)

*Actually, learning and/or understanding the math is not required to practice celnav. One can simply use pre-calculated tables and fill in pre-printed forms and do just fine. To be perfectly honest, I still don't completely understand it, myself.