My question concerns the ability to know the time that the redness of the sunset is no longer visible in the horizon. Is there a certain degree at which the redness/yellowness/whiteness disappears? I'm aware that the whiteness disappears at 18 degrees but i'm more interested in the redness.
To the best of my knowledge/understanding, there is no well defined angle at which these colors/light will disappear. In general the last light from the horizon would be red since it has to go through so much atmosphere and it would just fade to black. I don't think that there would be a specific angle, since that would depend on the amount of dust and particles in the air you're looking through which changes from place to place. So, for lack of a mathematical answer, I'd probably just measure it. I'd probably just wait till the sky was clear and then take digital pictures from Sunset on every minute. Then I'd measure how many pictures/minutes it took for the horizon to change from what I'd call “yellow” to “red” (this is probably the loss of more and more blue scattered light), then how many pictures it took for the red to fade out and be “gone”/black. Then you just have to convert your minute/picture counts to degrees. Each minute/picture is worth 0.25 degrees. So if one of those transitions was 32 pictures after sunset then it's 32×0.25=8 degrees. You said 18 degrees from the Sun the white faded. That's 18/0.25=72 minutes (1 hour and 12 minutes). So you're looking at 72 pictures at most.
I hope this helps. Sorry I couldn't give you an equation or a hard answer. But this is so complex and interesting a problem that it'd be easier to measure it.
Ryan Montgomery - UC Santa Cruz Astronomy Department