# SUN-EARTH GEOMETRY

Sun Earth geometry plays a important role in solar energy generation.One can not consider the solar energy without becoming aware of earth’s motion, both its rotational about its own axis and its orbital motion about the sun.These two modes of motion give rise to day and night, the number of hours of daylight, the angle of the sun in the sky, and the seasons.
The Earth’s daily rotation about the axis through its two celestial poles (North and South) is perpendicular to the equator, but it is not perpendicular to the plane of the Earth’s orbit. In fact, the measure of tilt or obliquity of the Earth’s axis to a line perpendicular to the plane of its orbit is currently about 23.5°. We call the plane parallel to the Earth’s celestial equator and through the center of the sun the plane of the Sun. The Earth passes alternately above and below this plane making one complete elliptic cycle every year.

### Vernal and Autumnal Equinox

There are two occasions throughout the year when the center of the Earth lies in the plane of the Sun.

Since the Earth’s North – South axis of rotation is perpendicular to this plane, it follows that on these two days every location on the Earth receives 12 hours of sunshine. These two events are known as the vernal and autumnal equinoxes.

In general, the Sun declination angle, δ, is defined to be that angle made between a ray of the Sun, when extended to the center of the earth, O,   and the equatorial plane. We take   δ   to be positively oriented whenever the Sun’s rays reach   O   by passing through the Northern hemisphere.

The Sun declination angle has measure:   δ = 0° on the days of   the vernal and the autumnal equinox.

### Summer Solstice

On the occasion of the summer solstice, the Sun shines down most directly on the Tropic of Cancer in the northern hemisphere, making an angle   δ = +23.5° with the equatorial plane.

On the day of the summer solstice, the sun is above the horizon for the longest period of time in the northern hemisphere. Hence, it is the longest day for daylight there.   Conversely, the Sun remains below the horizon at all points within the Antarctic Circle on this day.

### Winter Solstice

On the day of the winter solstice, the smallest portion of the northern hemisphere is exposed to the Sun and the Sun is above the horizon for the shortest period of time there. In fact, the Sun remains below the horizon everywhere within the Arctic Circle on this day. The Sun shines down most directly on the tropic of Capricorn in the southern hemisphere on the occasion of the winter solstice.

Sun Earth geometry parameter like declination angle affect the generation of solar energy. Accurate knowledge of the declination angle is important in navigation and astronomy. For most solar design purposes, however, an approximation accurate to within about 1 degree is adequate. One such approximation for the declination angle is:

sin δ   =   0.39795 ⋅ cos [ 0.98563 ⋅ ( N – 173 ) ]

where the argument of the cosine here is in degrees and N   denotes the number of days since January 1.

The Sun declination angle, δ,   has the range: – 23.5° < δ   <   + 23.5°   during its yearly cycle