NavList:

David,

>>The variation of the duration of twilight with declination is, in my opinion, harder to demonstrate pictorially.<<

But exactly that was under discussion! And it's easy to demonstrate: All you need to do is to draw a meridian in your Fig.1 through the point where the sun is cutting through the Small Circle labeled "-12". Done. You will immediately see that this meridian cuts the equator farther than 12 deg away from the terminator. The picture is actually easier to draw in the left diagram for the special case where lat = 0 than for the general case in the right diagram, where you have to draw two meridians (a second one through the terminator)!

It would seem to me that bringing latitude into play only adds confusion to the explanation. The effect of sun declination is one thing and that of observer latitude is another. Both are of a different nature, independent of each other, and have thus their individual explanation, as you can now see from the diagrams in Fig. 1, should you chose to complete them as per the above.

>> Interestingly, while the duration of twilight differs with changes in declination, it only does so at significant values of the observer’s latitude.  If the observer is at 0N/S the change in duration of twilight with declination is minimal, and the actual duration equates very roughly to the Earth’s rate of rotation of 15 degrees per hour.  <<

This is obviously wrong. The change is 2.15 min or 9%, (I mistakenly wrote 2min 15sec in my earlier message on this subject), pretty much in line with the numbers Norm Goldblatt gave for sunset, although Norm's numbers don't make perfect sense to me. May I ask here where they are coming from?

By the way, nautical twilight starts at the end of civil, i.e. when the sun is 6 deg under the horizon. I deliberately had suggested to look into this phenomenon in order to reduce the problem to a purely geometrical one; in other words, so that we don't get distracted by refraction or sun diameter.

I am actually a little surprised that we are having this discussion. Does no one besides astrologers use the concept of "equation of time"? I thought  navigators know it, too? What causes the EoT?

Herbert