## Friday, February 1, 2008

### Earth-Sun Geometry

Earth-Sun Geometry

Earth Rotation and Revolution
The term Earth rotation refers to the spinning of our planet on its axis. Because of rotation, the Earth's surface moves at the equator at a speed of about 467 m per second or slightly over 1675 km per hour. If you could look down at the Earth's North Pole from space you would notice that the direction of rotation is counter-clockwise (Figure 6h-1). The opposite is true if the Earth is viewed from the South Pole. One rotation takes exactly twenty-four hours and is called a mean solar day. The Earth’s rotation is responsible for the daily cycles of day and night. At any one moment in time, one half of the Earth is in sunlight, while the other half is in darkness. The edge dividing the daylight from night is called the circle of illumination. The Earth’s rotation also creates the apparent movement of the Sun across the horizon.

Figure 6h-1: The movement of the Earth about its axis is known as rotation. The direction of this movement varies with the viewer’s position. From the North Pole the rotation appears to move in a counter-clockwise fashion. Looking down at the South Pole the Earth’s rotation appears clockwise.

The orbit of the Earth around the Sun is called an Earth revolution. This celestial motion takes 365.26 days to complete one cycle. Further, the Earth's orbit around the Sun is not circular, but oval or elliptical (see Figure 6h-2). An elliptical orbit causes the Earth's distance from the Sun to vary over a year. Yet, this phenomenon is not responsible for the Earth’s seasons! This variation in the distance from the Sun causes the amount of solar radiation received by the Earth to annually vary by about 6%. Figure 6h-2 illustrates the positions in the Earth’s revolution where it is closest and farthest from the Sun. On January 3, perihelion, the Earth is closest to the Sun (147.3 million km). The Earth is farthest from the Sun on July 4, or aphelion (152.1 million km). The average distance of the Earth from the Sun over a one-year period is about 149.6 million km.

Figure 6h-2: Position of the equinoxes, solstices, aphelion, and perihelion relative to the Earth's orbit around the Sun.

Tilt of the Earth's Axis
The ecliptic plane can be defined as a two-dimensional flat surface that geometrically intersects the Earth's orbital path around the Sun. On this plane, the Earth's axis is not at right angles to this surface, but inclined at an angle of about 23.5° from the perpendicular. Figure 6h-3 shows a side view of the Earth in its orbit about the Sun on four important dates: June solstice, September equinox, December solstice, and March equinox. Note that the angle of the Earth's axis in relation to the ecliptic plane and the North Star on these four dates remains unchanged. Yet, the relative position of the Earth's axis to the Sun does change during this cycle. This circumstance is responsible for the annual changes in the height of the Sun above the horizon. It also causes the seasons, by controlling the intensity and duration of sunlight received by locations on the Earth. Figure 6h-4 shows an overhead view of this same phenomenon. In this view, we can see how the circle of illumination changes its position on the Earth’s surface. During the two equinoxes, the circle of illumination cuts through the North Pole and the South Pole. On the June solstice, the circle of illumination is tangent to the Arctic Circle (66.5° N) and the region above this latitude receives 24 hours of daylight. The Arctic Circle is in 24 hours of darkness during the December solstice.
Figure 6h-3:The Earth’s rotational axis is tilted 23.5° from the red line drawn perpendicular to the ecliptic plane. This tilt remains the same anywhere along the Earth’s orbit around the Sun.

Figure 6h-4: Annual change in the position of the Earth in its revolution around the Sun. In this graphic, we are viewing the Earth from a position in space that is above the North Pole (yellow dot) at the summer solstice, the winter solstice, and the two equinoxes. Note how the position of the North Pole on the Earth's surface does not change. However, its position relative to the Sun does change and this shift is responsible for the seasons. The red circle on each of the Earths represents the Arctic Circle (66.5 degrees N). During the June solstice, the area above the Arctic Circle is experiencing 24 hours of daylight because the North Pole is tilted 23.5 degrees toward the Sun. The Arctic Circle experiences 24 hours of night when the North Pole is tilted 23.5 degrees away from the Sun in the December solstice. During the two equinoxes, the circle of illumination cuts through the polar axis and all locations on the Earth experience 12 hours of day and night.

On June 21 or 22 the Earth is positioned in its orbit so that the North Pole is leaning 23.5° toward the Sun (Figures 6h-3, 6h-4, 6h-5 and see animation - Figure 6h-7). During the June solstice (also called the summer solstice in the Northern Hemisphere), all locations north of the equator have day lengths greater than twelve hours, while all locations south of the equator have day lengths less than twelve hours (see Table 6h-2). On December 21 or 22 the Earth is positioned so that the South Pole is leaning 23.5 degrees toward the Sun (Figures 6h-3, 6h-4, 6h-5 and see animation - Figure 6h-8). During the December solstice (also called the winter solstice in the Northern Hemisphere), all locations north of the equator have day lengths less than twelve hours, while all locations south of the equator have day lengths exceeding twelve hours (see Table 6h-2).
Figure 6h-5: During the June solstice the Earth's North Pole is tilted 23.5 degrees towards the Sun relative to the circle of illumination. This phenomenon keeps all places above a latitude of 66.5 degrees N in 24 hours of sunlight, while locations below a latitude of 66.5 degrees S are in darkness. The North Pole is tilted 23.5 degrees away from the Sun relative to the circle of illumination during the December solstice. On this date, all places above a latitude of 66.5 degrees N are now in darkness, while locations below a latitude of 66.5 degrees S receive 24 hours of daylight.

On September 22 or 23, also called the autumnal equinox in the Northern Hemisphere, neither pole is tilted toward or away from the Sun (Figures 6h-3, 6h-4, 6h-6 and see animation - Figure 6h-9). In the Northern Hemisphere, March 20 or 21 marks the arrival of the vernal equinox or spring when once again the poles are not tilted toward or away from the Sun. Day lengths on both of these days, regardless of latitude, are exactly 12 hours. Figure 6h-6: During the equinoxes, the axis of the Earth is not tilted toward or away from the Sun and the circle of illumination cuts through the poles. This situation does not suggest that the 23.5 degree tilt of the Earth no longer exists. The vantage point of this graphic shows that the Earth's axis is inclined 23.5 degrees toward the viewer for both dates (see Figures 6h-3 and 6h-4). The red circles shown in the graphic are the Arctic Circle.