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hen the clock is gaining on the sundial, the Sun rises and sets later each day, and when the sundial is gaining on the clock, the Sun rises and sets earlier each day. If the two effects which give us the equation of time were solely responsible for sunrise and sunset times, these times would be late in summer and winter and early in spring and fall. Most of us would say at once that, of course this is not true. But it is true for anyone living on the equator!

On a standard meridian at the equator one might expect the Sun to rise at 6:00 A.M. and set at 6:00 P.M., but the Sun rises at 6:03 A.M. in July, a summer month, and also rises late, at 6:11 A.M. in February, a winter month. It rises seven minutes before 6:00 A.M. in mid-May, and 20 minutes before 6:00 A.M. at the end of October. At the equator these effects are entirely accounted for by the equation of time.

The daily path of the Sun as seen at the equator on the first day of spring, summer, fall, and winter is illustrated in Figures 7 and 7a . At the equator the Sun rises perpendicularly from the horizon and sets perpendicularly, regardless of the season. Also, the total path of the Sun, day and night, is divided equally by the horizon. There are always twelve hours of daytime and twelve hours of night-time at the equator, except for two minor effects that increase daytime by about eight minutes. First, since we mark the instant of sunrise as the time the Sun's upper edge or "limb" just touches the horizon, the actual center of the Sun is still below the horizon by half the diameter of the Sun, 16 arc minutes or degree.. It will take an additional minute for the Sun's center to be on the horizon. At sunset the same thing happens and so an additional two minutes are gained for daytime. Second, when the Sun's limb appears at the horizon, it is actually still 43 arc minutes below the horizon but only appears to be at the horizon due to the refraction or bending of the Sun's rays by the Earth's atmosphere. This effect causes the sunrise to appear about three minutes early and sunset late by the same amount. Taking both effects together, the length of daytime is about 8 minutes more than 12 hours, and so, of course, night-time will be 8 minutes less than 12 hours, resulting in daytime being 16 minutes more than night-time at the equator, or for that matter, anywhere during the equinoxes (March 21 and September 21).

Figure 7. The daily or diurnal paths of the Sun during the solstices(21 December and 21 June) and the equinoxes (21 March and 21 September) as seen by an observer at the equator. Solid lines are daytime, dashed lines are night-time. At all seasons on the equator, the daily paths of the Sun are divided equally above and below the horizon.

The same information shown in Figure 7 is presented in Figure 7a, below, in the form of a polar plot of the position of the Sun in the coordinates of the azimuth and altitude of the Sun as seen by an observer at that latitude.

Figure 8 and 8a show the apparent paths of the Sun as seen from Hawai'i, the southernmost State of the United States, 21 degrees north of the equator. The paths are all parallel to each other, but are slanting at 21 degrees to the horizon. It will also be noticed that the horizon divides the total path of the Sun into equal periods only on the first days of spring and fall, i.e., the equinoxes. In summer, the portion of the Sun's path above the horizon is much greater than the night portion, and the reverse is true in the winter. This illustrates the geographical effect, which depends on the observer's latitude.

Figure 8 and 8a (below). The daily path of the Sun as seen from Hawai'i on the first day of spring, summer, fall, and winter.

An extreme situation is shown in Figures 9 aand 9a for a location at the Arctic Circle, latitude 66 o north. The Sun is above the horizon all day at the beginning of summer, barely touching the horizon at midnight.

At the beginning of winter the Sun's path is entirely below the horizon. This latter situation is modified by the refraction of sunlight by the Earth's atmosphere which causes the Sun to appear a little higher at the horizon than it actually is. Because of this refraction, the Sun appears briefly above the southern horizon at noon on the first day of winter at the Arctic Circle.

Figures 9 and 9a (below). The daily path of the Sun as seen at 66.5 degrees north latitude (the Arctic Circle) on the first day of spring, summer, fall, and winter.


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