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(c)
RENOVETEC 2010. All right reserved
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Solar Geometry
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Español
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.
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.
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.
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).
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.
Axis Tilt and Solar Altitude
The annual change in the relative position of the Earth's axis in
relationship to the Sun causes the height of the Sun or solar altitude
to vary in our skies. Solar altitude is normally measured from either
the southern or northern point along the horizon and begins at zero
degrees. Maximum solar altitude occurs when the Sun is directly
overhead and has a value of 90°. The total variation in maximum solar
altitude for any location on the Earth over a one-year period is 47°
(Earth’s tilt 23.5° x 2 = 47°). This variation is due to the annual
changes in the relative position of the Earth to the Sun. At 50 degrees
North, maximum solar altitude varies from 63.5 degrees on the June
solstice to 16.5 degrees on the December solstice (Figure 6h-10).
Maximum solar height at the equator goes from 66.5 degrees above the
northern end of the horizon during the June solstice, to directly
overhead on the September equinox, and then down to 66.5 degrees above
the southern end of the horizon during the December solstice (Figure
6h-11).
he location on the Earth where the Sun is directly overhead at solar
noon is known as the subsolar point. The subsolar point occurs on the
equator during the two equinoxes (Figures 6h-11 and 6h-12). On these
dates, the equator is lined up with the ecliptic plane and the poles
are in line with the circle of illumination (Figure 6h-6). During the
summer solstice, the subsolar point moves to the Tropic of Cancer
(23.5° N) because at this time the North Pole is inclined 23.5° toward
the Sun (Figures 6h-12 and 6h-13). Figure 6h-13 shows how the subsolar
point gradually changes from one day to the next over a period of
one-year. Note that on this graph, the subsolar point is located at the
Tropic of Capricorn (23.5° S) during the December solstice when the
South Pole is angled 23.5° toward the Sun (Figure 6h-5).
The following table describes the changes in solar altitude at solar
noon for the two solstices and equinoxes. All measurements are in
degrees (horizon has 180 degrees from True North to True South) and are
measured from either True North or True South (whatever is closer).
The following links show graphical illustrations of the annual
movements of the Sun in our skies for selected latitudes. In these
illustrations, solar angles are measured from both True North and True
South for solar noon.
| 90 N | 66.5 N | 50 N | 23.5 N | Equator (0) | 23.5 S | 50 S | 66.5 S | 90 S |
Finally, the altitude of the Sun at solar noon can also be calculated with the following simple equation:
Altitude A = 90 - Latitude L +/- Declination D
In this equation, L is the latitude of the location in degrees and D is
the declination. The equation is simplified to A = 90 - L if Sun angle
determinations are being made for either equinox date. If the Sun angle
determination is for a solstice date, declination (D) is added to
latitude (L) if the location is experiencing summer (northern latitudes
= June solstice; southern latitudes = December solstice) and subtracted
from latitude (L) if the location is experiencing winter (northern
latitudes = December solstice; southern latitudes = June solstice). All
answers from this equation are given relative to True North for
southern latitudes and True South for northern latitudes. For our
purposes only the declinations of the two solstices and two equinoxes
are important. These values are: June solstice D=23.5, December
solstice D=23.5, March equinox D=0, and Septemeber equinox D=0. When
using the above equation in tropical latitudes, Sun altitude values
greater than 90 degrees may occur for some calculations. When this
occurs, the noonday Sun is actually behind you when looking towards the
equator. Under these circumstances, Sun altitude should be recalculated
as follows:
Altitude A = 90 - (originally calculated Altitude A - 90)
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(c) RENOVETEC
2010. All right reserved
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