1 3. Basic principles of solar geometry Petros Axaopoulos TEI of Athens Greece Learning Outcomes After studying this chapter, readers will be able to: ° understand the sun-earth geometry and the basic solar geometry angles ° perform various calculations between solar angles ° distinguish the difference between solar and local time ° define the position of the sun in relation to the earth ° explain the diurnal and annual apparent path of the sun’s motion ° calculate the solar incidence angle for a plane oriented and tilted arbitrarily relative to the earth This chapter describes the sun-earth geometry and how it can be used to define the position of the sun in relation to the earth. For the solar energy applications, it is important to understand the apparent motion of the sun, as well as the sun-earth angles. Understanding this mechanism will be of importance in the following chapters, which include elementary notions of astronomy. Thus, the emphasis is on the notions and terms that concern the sun-earth angles and their interrelationships, which are of high importance in solar geometry. 3.1 The Earth’s rotation The earth rotates around its own axis, known as the Polar Axis P P ' (Fig. 3.1). The points at which this axis intercepts the earth are the north (N p ) and the south (S p ) poles. The great circle EΙWΙ ' normal to this axis is called equator and the plane containing the equator is the equatorial plane that divides the earth in northern and southern hemisphere. The great circle ESWN normal to the axis ZZ ' is called horizon. The position of the sun in the sky varies throughout the day and season due to the rotation of the earth around its axis once per day. Similarly, it changes its elliptical orbit around the sun, once per year, with the sun at one focus of the ellipse (Fig. 3.2).
2 Ζ Z’ Π Π ’ Ι I’ Β Ν Α ∆ Figure 3.1 Horizon and equatorial plane Figure 3.2 Rotation of the earth around its axis and its elliptical orbit around the sun The plane containing the earth’s elliptical orbit is called the ecliptic plane. The
3 seasons are due to the fact that the earth’s axis, which is perpendicular to the equatorial plane, is inclined with respect to the ecliptic plane (Figure. 3.3). Figure 3.3 Equatorial and ecliptic plane Also, ecliptic can be defined as the apparent path of the sun’s motion on the celestial sphere as seen from earth. The points γγ΄ the ecliptic plane intersects the equatorial plane of the celestial sphere are called equinoxes. These points determine the dates that have 12 hours each of daylight and dark. The most northern excursion of the sun is called the summer solstice and will have the longest amount of daylight. The winter solstice opposite is the shortest period of daylight.
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