Sunrise and Sunset
The paths of the sun, moon, and stars are circles centered on the north and south poles of the sky. If the object is on the equator, as the sun is on the first day of spring and the first day of fall, this circle is 90 degrees from the pole and goes through the east and west points on the horizon. If the object is north of the equator, the circle parallels the equator as many degrees north of the former circle as the object is north of the equator. The reverse is true for an object that is south of the equator.

For a location that is on the geographical equator, the poles are on the horizon, so all of the circles are perpendicular to the horizon and the size of the circles does not change greatly with the position of the object until you get quite near the poles. At any location north of the equator,  the north pole is as many degrees above the horizon as the latitude is north of the geographical equator. For southern latitudes, the south pole is above the horizon. For a location very far north, as is Fairbanks, all of the circles are tilted less strongly to the horizon and the length of the arcs above the horizon vary significantly with the position of the object.
 
 
 
 
 
 
 
 

The atmosphere acts somewhat as a lens. Near the horizon, it raises the images slightly. As a result when we see the sun begin to set, the sun is really slightly below the horizon. Thus, when the sun is on the equator, it is apparently above the horizon for more than 12 hours.

Many years ago, each city used its own time. Noon was when the sun was due south. When the railroads became popular, this created many problems. To simplify determining the time in another city, most of the world was divided into standard time zones. Each zone is 15 degrees in longitude wide. For each fifteen degrees that one moves west of Greenwich, England, the time is one hour earlier. Columbus and Washington, DC are both in the Eastern time zone but the sun is at a given position 24 minutes later in Columbus because Columbus is 6 degrees west of Washington.

The orbit of the earth around the sun is nearly a circle, but not quite. The earth moves faster in its orbit when it is nearer the sun, as it is in the northern winter. Thus, in winter, the sun gets somewhat ahead of schedule and the sunset times begin to become later while the sunrise times are still becoming later also. This deviation of sun time from a uniform time is known as the "equation of time".

The orbit of the moon around the earth is also not quite a circle. Moreover, it is tilted 18 degrees with respect to the equator of the earth. Both of these effects cause the length of the month to vary slightly with time.