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A few days ago I mentioned that it is staying twilight until really late. My friend Jason pointed out on facebook today that as of yesterday the Sun no longer goes lower than 18° below the horizon. By the definitions given by the U.S. Naval observatory, this means that at the darkest part of the night we are officially in ‘astronomical twilight’.
Astronomical twilight is defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 18 degrees below the horizon. Before the beginning of astronomical twilight in the morning and after the end of astronomical twilight in the evening the Sun does not contribute to sky illumination; for a considerable interval after the beginning of morning twilight and before the end of evening twilight, sky illumination is so faint that it is practically imperceptible.
USNO Rise, Set, and Twilight Definitions
I took a few screenshots from Stellarium to illustrate the geometry:
If you take away the ground, the ‘elevation’ of the Sun behind the horizon can be seen:
As we move toward summer solstice the Sun will keep getting closer and closer to the horizon until it is only about 2° below the horizon. If you drive a little further north to the arctic circle the Sun won’t even set, it will just do a little bounce off the horizon on the solstice.