Originally Posted By: wfaulk
It should approximate the amount of time of twilight, or maybe double that, starting when the sun starts to go below the horizon. (Seems like there ought to be a technical word for that, but I can't find it.)

The Right Answer, of course, is for flux to work out the Earth's orbital parameters, and thus the sun angles, using the JPL ephemeris. And you'll be pleased to hear that the JPL page describing various revisions of this calculation refers to them as "ephemerides".

Peter