NavList:

Sean,

You wrote: "is this a reasonable way to approximate twilight times?"

It's not just a reasonable approximation. That's exactly how it's done. You reverse-engineered it perfectly as far as I can tell. Bravo! I didn't proofread every little detail of what you did, but reading it through normally, yes, that's what the twilight numbers in the almanacs mean. You've got the principle exactly right. All you do is find the time when the Sun's geocentric altitude is -6° for civil, -12° for nautical, and -18° for astronomical twilight. Determining that time is just a matter of calculating the LHA for those three altitudes for a given latitude and declination of the Sun and then converting that to local zone time using the steps you've described. There's really nothing more to it. If you want to test your procedures, try some high latitudes. For example, what are the times of the various twilights in Alaska on the summer solstice?

Greg Rudzinski suggested that the almanac calculations are more complicated, and they could have been, but that actually isn't the case. There's no need to complicate matters. The times of twilight are arbitrary definitions that were adopted some decades ago (an interesting bit of historical trivia to uncover: when did that arbitrary definition become common?), and the effects of refraction and so on really don't enter into it. So, for example, twilight durations should be much shorter on top of Mount Everest --we know that twilight is much quicker in thin air-- but there's no provision for this in any calculation of twilight. Notice that the arbitariness of these twilight definitions and their limitation to sea level conditions is rather similar to the standardized definition that we use for the times of sunrise and sunset. They, too, assume an observer at sea level (literally at sea level --with zero height of eye) and allow for no variation in observing conditions.

-FER