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.