E.1
E
Some aspects on location issues
In Section E.1 we will derive the equations, which are used to calculate the position of the
Sun in the horizontal coordinate system that is illustrated in Figure 18.1. In Section E.2,
we will discuss the equation of time. The last two sections are devoted to calculating the
cosine between PV modules and the Sun: in Section E.3 this is done for modules installed
on a horizontal plane while in Section E.4 the more complex case of PV modules on a roof
is treated.
The position of the Sun
Earth orbits the Sun in an elliptic orbit at an average distance of about 150 million
kilometres. Due to the elliptic orbit the speed of Earth is not constant, which is described
by Kepler’s second law, named after Johannes Kepler (1571-1630). It states that ‘A line
joining a planet and the Sun sweeps out equal areas during equal intervals of time.’ On the
celestial sphere the Sun seems to move on a circular path with one revolution per year.
This path is called the ecliptic and illustrated in Figure E.1. To describe the apparent
movement of the Sun on the celestial sphere it is convenient to use coordinates in which
the ecliptic lies in the fundamental plane. This coordinate system is called the ecliptic
coordinate system; it is shown in Figure E.2 (a). The principal direction of this coordinate
system is the position of the Sun at the spring (vernal) equinox (thus around 21 March) is
used, which is indicated by the sign of Aries, . As is obvious from Figure E.1, lies in
both the ecliptic and the equatorial planes. The two angular coordinates are called the
ecliptic longitude λ and the ecliptic latitude β. Note, that in this coordinate system the
rotation of the Earth around its axis is not taken into account.
In ecliptic coordinates the position of the Sun can be expressed easily. The
approximation presented here has an accuracy of about 1 arcminute
1 within two centuries
around the year 2,000 and is published by the Astronomical Applications Department of
the US Naval Observatory [200].
E
Some aspects on location issues
In Section E.1 we will derive the equations, which are used to calculate the position of the
Sun in the horizontal coordinate system that is illustrated in Figure 18.1. In Section E.2,
we will discuss the equation of time. The last two sections are devoted to calculating the
cosine between PV modules and the Sun: in Section E.3 this is done for modules installed
on a horizontal plane while in Section E.4 the more complex case of PV modules on a roof
is treated.
The position of the Sun
Earth orbits the Sun in an elliptic orbit at an average distance of about 150 million
kilometres. Due to the elliptic orbit the speed of Earth is not constant, which is described
by Kepler’s second law, named after Johannes Kepler (1571-1630). It states that ‘A line
joining a planet and the Sun sweeps out equal areas during equal intervals of time.’ On the
celestial sphere the Sun seems to move on a circular path with one revolution per year.
This path is called the ecliptic and illustrated in Figure E.1. To describe the apparent
movement of the Sun on the celestial sphere it is convenient to use coordinates in which
the ecliptic lies in the fundamental plane. This coordinate system is called the ecliptic
coordinate system; it is shown in Figure E.2 (a). The principal direction of this coordinate
system is the position of the Sun at the spring (vernal) equinox (thus around 21 March) is
used, which is indicated by the sign of Aries, . As is obvious from Figure E.1, lies in
both the ecliptic and the equatorial planes. The two angular coordinates are called the
ecliptic longitude λ and the ecliptic latitude β. Note, that in this coordinate system the
rotation of the Earth around its axis is not taken into account.
In ecliptic coordinates the position of the Sun can be expressed easily. The
approximation presented here has an accuracy of about 1 arcminute
1 within two centuries
around the year 2,000 and is published by the Astronomical Applications Department of
the US Naval Observatory [200].