JSCzepek --
It's a very interesting question. The phenomenon is fairly well-known
to pilots and can be related to a mathematical function -- the curve
for a sine wave.
You'll note that the "civil" definition of twilight is when the sun is
less than 6 degrees below the horizon; while the nautical definition
continues twilight to continue up to 12 degrees. Astronomical
twilight continues up to 18 degrees, as star-gazers are seeking the
darkest night skies:
EOpinions.com
CityTime: Choose Your Time (Feb. 11, 2001)
http://www.epinions.com/content_8870203012
Sidell Personal Home Page
"Moonrise site" (undated)
http://www.iserv.net/~bsidell/moonts.htm
The time that the sun takes to slip that far beneath the horizon is
relatively constant at the Equator. Also the angle of the sun's
setting is near perpendicular.
However, the Earth's angle to the sun creates different lengths of
days during summer and winter seasons. For exmple, in northern
latitudes during the summer, the sun slides beneath the horizon at an
angle. At the most-northern latitudes, above the Arctic Circle, in
late June the sun won't even drop below the horizon:
NASA Goddard Space Flight Center
"What is the difference between civil twilight, nautical twilight and
astronomical twilight?" (Oct. 13, 1997)
http://www.gsfc.nasa.gov/gsfc/educ/science/1998/10-13-97.htm
Here's a graphical representation of what happens:
Skywise
"Length of Twilight" (Sky & Telescope, August, 1998)
http://www.mangobay.cc/users/moonfinder/aug-98.htm
In effect, you find that the sun's angle to the horizon is behaving
like a sine curve at the Summer Solstice -- with the Equator having an
angle like a sine curve at zero degrees and the angle becoming more
shallow until the North Pole (similar to the 90-degree point). But,
of course, the angle is changing daily.
Google strategy:
"twilight calculations"
"length of twilight"
Now, I have to relate a personal story. In the 1970s, I taught high
school math and physics in Zaire. In the summer of 1974, my roommate
and I were traveling on bicycle to Kisangani. Our first night was
spent in a small town called Kipaka, where we were guests of another
teacher's family. We spent the evening talking with people about
satellites (called "stars that walk" in Swahili), Americans traveling
to the moon, and what snow is like. The people in this farming town
were very curious and receptive to what one had to say.
However, when we explained that in the summertime in the U.S. the days
can go from 5:30 a.m. to 10 p.m., we were told, "Oh monsieur, we may
be simple farmers, but not even we are foolish enough to believe a
story like that!"
Kipaka is about 4 degrees south of the Equator (near Kasongo, Zaire)
and the changes in days were so slight as to be unnoticed. Of course
twilight was brief all year long.
Best regards,
Omnivorous-GA |
Request for Answer Clarification by
jsczepek-ga
on
24 Jan 2004 09:40 PST
But I still do no understand what both described cases have in common.
In the first case, the sun stays vertical to the horizon and I move
north through the latitudes and encounter increasing twilight
duration, and in the second I stay at, say, 40° north 0° west and
encounter increasing twilight duration as the sun moves north from
vernal equinox to summer solstice. It could well be that I just have a
knot in my brain, but I donīt see it ! - Does the angle between the
sunīs orbit and the respective horizon change so that the curve gets
shallower ? And what is about the significant difference in the
duration of twilight between the vernal equinox and the autumnal
equinox, although the sun is in verical position above the equator in
both cases.
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