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or a time before sunrise and after sunset, light from the Sun illuminates the atmosphere to produce some skylight, known as twilight. Twilight is arbitrarily divided into three increments. The period when the Sun is 6 degrees or less below the horizon is called civil twilight . The time of the end of civil twilight is often published in newspapers along with the time of sunrise and sunset. When the Sun is between six and twelve degrees below the horizon, the period is called nautical twilight. During this period it is dark enough to see the brighter stars, used for navigation, and still light enough to see the horizon. When the Sun is between twelve and eighteen degrees below the horizon, the period is called astronomical twilight.

Further inspection of figures 7, 8, and 9 reveals that the time for the Sun to reach these twilight angles differs at different seasons. At the equator, the evening Sun reaches the position ending civil twilight in only 23 minutes. In Hawai'i, civil twilight lasts 27 minutes in winter and 28 minutes in summer. At 45 degrees latitude the same period is 35 minutes in winter and 37 minutes in summer.

The more popular concept of twilight more nearly matches the period of nautical twilight, and the effect of latitude is more pronounced for this period. In Hawai'i, nautical twilight ends 52 minutes after sunset in winter and 55 minutes after sunset in summer. At 45 degrees latitude, the corresponding periods are 73 minutes in winter and 85 minutes in summer. the longer hours of twilight at higher latitudes contribute to the acceptability of daylight saving time. In London, England, 51 degrees north, on the first day of summer, the Sun sets at 8:18 P.M., and nautical twilight ends nearly two hours later, at 10:16 P.M. Only a little farther north, latitude 54 o , nautical twilight runs through midnight, lasting all night long in summer. At the Arctic Circle, while the Sun is below the horizon for long periods in the winter months, much of its path is within the nautical twilight zone below the horizon , so that twilight lasts most of the day even on the first day of winter. The portion of night-time hours that receives some illumination, through nautical twilight, is shown in Fig. 10.

Figure 10. Seasonal and geographic variations in daylight, twilight, and dark night hours.

Figure 10 also summarizes the results of the previous section on Sunrise and Sunset. The larger seasonal change in daylight hours at 45 degrees latitude over that at the latitude of Hawai'i, reveals the advantage of "daylight saving time" in northern cities where the summer daylight period is so long. In Hawai'i, the daylight period is more nearly the same all year around. Shifting the clocks in Hawai'i can only rob the short morning hours to give extra daylight in the evening. Hawai'i does not have the morning hours to spare. At the time of this writing, Hawai'i does not observe "daylight time."

A seemingly contradictory condition in the time of sunrise is often noted by critical observers. In the northern hemisphere the shortest day of the year is the first day of winter, December 21. Yet the time of sunrise continues to grow later into early January when the duration of the daylight period is actually lengthening. The reason is that this is the time of the year when the equation of time still dominates the seasonal effect, causing both sunrise and sunset to occur later each day. (See NOTE below). This effect is greater for locations near the equator. In Hawai'i, at 21 o north, the latest sunrise is January 15, twenty-five days after the winter solstice, the shortest day of the year. At 45 degrees north latitude, the latest sunrise occurs on January 3, and in London, at 51 degrees north, the latest sunrise is on December 31. The annual variations in sunrise and sunset times at these latitudes are illustrated in Fig. 11. The large differences in seasonal times of sunrise and sunset as well as differences at different latitudes may be seen in this figure . It may be noted that, at higher latitudes, the observation of "daylight saving time" is of far greater value than nearer the equator. Furthermore, the additional morning and evening twilight greatly extends the total "daylight" at higher latitudes.

Figure 11. The annual variations in sunrise and sunset times at various locations: 0o (equator), 21o20' (Honolulu), 45o (Minneapolis), 51o (London).

NOTE: Reader Johan Demoen ( of Hove, Belgium, has this to say about the phenomenon: "My idea is that the equation of time is not a cause but a result of some astronomical fact. The real reason of this strange behaviour of the sunrise, c.q. sunset between approximately 21 december and 3 januari lies in the fact that the moment of maximum negative declination of the Sun (+- 21 december ) does not coincide with the moment of perihelion (and mutatis mutandis maximum positive declination and aphelion). On 21 december the plane defined by the axis of the Earth and the radius of the orbit is perpendicular to the orbit of the Earth. At that moment the points of intersection of the plane perpendicular to the axis of the Earth and going through the center of the Earth , with the plane of the local horizon, are perfectly symmetrical in relation to local true South. After 21 december these points of intersection are no more symmetrical to local true South, in so far that the "left" point continues to go south while the "right" point already starts to go west , but the left point is going slower south than the right point is going west , i.e. the length of the day is already increasing. After perihelion the left point starts to go east and the phenomenon is no more observable, but the hysteresis is still remains. ( All considerations to adapt to aphelion etc.)." Johan Demoen  

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