# Astronomical Investigation to Verify the Calendar Theory of the Nasca Lines
## 2 The Sun Worship in Pre-Columbian Cultures on the Current Territory of Peru  
### Astronomical Background  
There is evidence that most of the cultures on the territory of today's Peru worshiped the Sun. In this context, the alignment of structures to solstice events and equinoxes plays a major role because both solstices and equinoxes have been celebrated by many cultures throughout human history.  
Two solstices occur annually around 21 June and 21 December and these are the times of the astronomical beginning of summer and winter. Equinoxes are the calendar days on which the Sun crosses the celestial equator and therefore day and night are about the same length. The equinoxes are the times of the astronomical beginning of spring or autumn. However, when we talk about summer and winter solstices, we have to consider that these terms are ambiguous, since summer in the Northern Hemisphere is winter in the Southern Hemisphere and vice versa. The same applies to the spring and autumn equinoxes. Therefore, in the following, we use the terms December or June solstice and March or September equinox.  
A solstice is an event that occurs when the Sun reaches its greatest north or south declination in the course of a solar year. The declination \(\delta\) is one of the two angles that locate a point on the celestial sphere in the so-called equatorial coordinate system (Figure 4a). It is measured perpendicular, north or south, to the celestial equator. The other one is the right ascension \(\alpha\). It is the angular distance measured eastward along the celestial equator from the vernal equinox to the point in question above the Earth.  
Figure 4: (**a**) Equatorial coordinate system: right ascension \(\alpha\) and declination \(\delta\) as seen from outside the celestial sphere; (**b**) horizontal system: the coordinates of a celestial body are expressed in terms of the elevation angle h and azimuth a, which depend on the position of the observer O on Earth.  
An astronomical coordinate system that is frequently used to observe celestial bodies from the Earth is the local horizontal system (see Figure 4b) because this is based on the position of the observer on Earth and uses the observer's local horizon as the fundamental plane. The coordinates of a celestial body are expressed in terms of the altitude (or elevation angle) h and azimuth a. The altitude h is the angle between the object and the observer's local horizon, while the azimuth a is the angle usually measured clockwise from true north around the observer's horizon.  
The determination of the declination \(\delta\) of any object is given by the well-known formula  
\[\sin\delta=(\sin\,\varphi\,\sin\,\mathrm{h}+\cos\,\varphi\,\cos\,\mathrm{h}\, \cos\,\mathrm{a}) \tag{1}\]  
For an altitude h = 0\({}^{\circ}\) (Horizon), it follows  
\[\sin\delta=\cos\,\varphi\,\cos\,\mathrm{a} \tag{2}\]  
Hence, the astronomical azimuth of the sunrise or sunset on the ideal horizon (altitude h = 0\({}^{\circ}\)) is obtained from a simple equation:  
\[\mathrm{a}=arccos\bigg{(}\frac{\sin\delta}{\cos\,\varphi}\bigg{)} \tag{3}\]  
where the declination of the Sun is \(-23.5^{\circ}<\delta<+23.5^{\circ}\) and \(\varphi\) is the latitude of the position of the observer. The maximum declination of 23.5 degrees corresponds to the solstice in June; the minimum \(-23.5\) degrees is reached at the solstice in December. With a declination of 0\({}^{\circ}\), we speak of the equinox.  
For Peru, the mean latitude is \(-9.189967\) degrees and thus the approximate azimuth of the sunrise during the June solstice is around 66 degrees, while the sunset is at 294 degrees. On the other hand, during the December solstice, the sunrise is at approximately 114 degrees, while the sunset is at 246 degrees. The azimuth of the sunrise on the equinoxes is 90 degrees, and it is 270 degrees for the sunset.  
Both solstice events and equinoxes played an important role in pre-Columbian cultures. This is particularly reflected in their buildings and structures, as the following examples are intended to show.