By Doug Criner

Poets and songwriters have written profusely about day, night, morning, and evening—but much less so about twilight.  Recent travel to the tropics demonstrated to me the relatively shorter duration of tropical twilight compared to more northern latitudes, heightening my interest in the subject.

By definition, the duration of “civil” twilight is the time interval between sunrise (or sunset) and when the center of the sun is 6º below the horizon.  (See the U.S. Naval Observatory’s website at:  http://www.usno.navy.mil/USNO/astronomical-applications/astronomical-information-center/rise-set-twi-defs .)  Other definitions apply to “nautical” and “astronomical” twilight, but “civil” twilight would  generally be that period between perceived darkness and sunrise or sunset.

A potentially confusing issue is that while twilight begins or ends when the center of the sun is 6° below the horizon, sunset and sunrise occur when the sun’s upper limb is tangent to the horizon; the difference is important because the sun itself subtends an arc of about 0.5° in the earth’s sky.

The shortest twilight duration is about 21 minutes.  Consider an observer at the equator on March 20, the equinox—the sun circumscribes a circular arc, passing directly overhead at noon, and plunging into the horizon at sunset (not quite perpendicular, but let’s assume it is).  The earth rotates 0.25°/min, so you might calculate the twilight length as 6°/(0.25°/min) = 24 min.  However, sunrise or sunset are defined to occur when the sun’s upper limb is tangent to the horizon, not when the sun’s center is tangent; since the sun’s radius, as viewed from the earth, subtends about 0.27°, the sun’s center needs to travel only about 6 – 0.27 = 5.73° during twilight.

But wait, there’s more:  due to atmospheric diffraction, the sun’s upper limb appears tangent to the horizon when it is actually about 0.57° below the horizon.  So, the sun needs to travel only 6 – 0.27 – 0.57 = 5.16° during twilight; this takes 5.16°/(0.25°/min) = 20.6 minutes, which is the shortest twilight possible.

Now, let’s calculate the length of twilight in Chicago on the same date, March 20, the spring equinox.  As calculated above, the length of twilight at the equator is 20.6 minutes. Let’s adjust this for Chicago.

The sun’s noontime altitude in Chicago will be equal to the complement of Chicago’s latitude, 90 – 41.85° = 48.15°, and we can roughly estimate that at sunset, the sun will disappear, making that angle with the horizon.  If so, we can compute the length of twilight in Chicago as (20.6') / sin(48.15°) = 27.7'.  (The correct answer, per the U.S. Naval Observatory, is 28'; the Naval Observatory reports such astronomical data to the nearest whole minute.)

 Personal Observations

Based on my casual observations, the shorter tropical twilight durations are much more pronounced and the transition to darkness more sudden than might be inferred from the above astronomical data, e.g., 33 minutes versus 25 minutes.  My qualitative, unscientific perception of tropical sunsets is, “Who turned out the lights?”  Is this perception due to some innate human sensibility?  Or, is there some astronomical explanation that I have overlooked?  My perception could be validated with incident light measurements. 

It is interesting to speculate about the possible ramifications of shorter twilight in the tropics.

One practical implication involves celestial navigation, which admittedly is seldom used now that GIS is available.  As an “ancient mariner,” I learned that “shooting the stars” requires two things:  that stars be visible and, also, a very sharply defined horizon; both conditions occur simultaneously only briefly in dim twilight.  A shorter twilight period would provide less time for a navigator to do his work with precision.  Was the incidence of shipwrecks higher in the tropics?

Some wildlife may be more active during twilight periods.  Eastern U.S. songbirds come to mind.  (It would be interesting to study whether songbirds start their singing at a particular light level or based on the “real” position of the sun, which may be obscured by clouds.)  I suspect that owls, with their sharp vision, are more productive hunters in twilight.  Conceivably, shorter twilights may play a role in the evolution and adaptation of animals. 

Shorter twilights might have affected the development of human behavior.  The sudden onset of darkness in the tropics would have provided less leeway in returning home at night, and might have encouraged the development of time measurement devices. 

Another theory:  sudden and dramatic transition from light to dark might have prompted ancient peoples to be more obsessed with sun worship and astronomy.  For example, one thinks of the Maya in Central America.  For this observer accustomed to higher latitudes, tropical sunsets prompt feelings of mystery, awe, and spookiness.            

Twilight:  many questions to answer.

Addendum - thanks to Beverly King for advising me of this helpful site: http://osr.org/en-us/articles/a-closer-look-at-rise-set-and-twilight/

© 2010 Doug Criner