Geometry of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 10

X axis, the southern hemisphere. The Prime Meridian divides the area to the
right of the Y axis, the eastern hemisphere, from the area to the left of the Y
axis, the western hemisphere. Any x value to the right, or east, of the Y axis is
positive. Therefore, any longitude in the eastern hemisphere is positive. Any
x value to the left, or west, of the Y axis is negative. Therefore, any longitude
in the western hemisphere is negative. Similarly, any Y value above, or north,
of the X axis is positive. Therefore, any latitude in the northern hemisphere
is positive. Any Y value below, or south, of the X axis is negative. Therefore,
any latitude in the southern hemisphere is negative.

Thus, given the following coordinate pairs, one can determine their correct
hemisphere:

X, Y Eastern and northern hemisphere

−X, Y Western and northern hemisphere

X, −Y Eastern and southern hemisphere

−X, −Y Western and southern hemisphere

Therefore, all of the United States is in the northern hemisphere and is com-
posed of positive Y values in terms of latitude. Most of the United States is in
the western hemisphere, and is described with negative X values. The only
exception is the far western part of the Aleutian Islands, which extends into
the eastern hemisphere.

1.3 Theory: Earth's seasons—A visual display

The primary cause of Earth's seasons is the tilt of the Earth's polar axis in rela-
tion to the plane of the ecliptic (Sun's equatorial plane). The tilt is 23.5 degrees
and this tilt has far-reaching implications. Figure 1.8 illustrates the annual revo-
lution of the Earth around the Sun on the plane of the ecliptic. Note the constant
tilt of the Earth's polar axis. The circle of illumination, or terminator, marks the
separation of day and night. At the equinoxes (about March 21 and September
21), the circle of illumination passes through both poles (the only time of the
year at which it does so). Thus, at those times, the circle of illumination bisects
all parallels of latitude; half of the day is on the dark side, half of the day is on
the light side for all latitudes. Hence, “equinox = equal night” occurs all over the
world. On or about June 21, the northern half of the Earth receives the most
extra sunlight that it will all year-due to the axis tilt. Thus, it is the beginning of
summer (relatively warm season) in the northern hemisphere. It follows, there-
fore, that the southern half of the Earth on or about June 21 receives less sun
than on the equinox. Thus, it is winter in the southern hemisphere beginning on
or about June 21. Similar arguments apply on or about December 21.

As shown in Figure 1.8 , the North Pole is in constant darkness on December
21. Hence, it is the beginning of winter in the north and consequently sum-
mer in the south, on that date. The summer and winter positions are called