# Astronomical Investigation to Verify the Calendar Theory of the Nasca Lines
## 3 Astronomical Investigations in the Nasca Project
### Requirements for the Astronomical Investigations  
In order to prove whether the ancient lines in the desert near Nasca show a preference for the directions of the Sun, the Moon, planets or brighter stars, a fully automatic procedure is necessary. The very first step for this research was the geodetic data acquisition of all the lines, line centers, areas, figures and remarkable point objects (e.g., stone heaps) at a reliable accuracy. These data have been captured over the years using highly accurate measurement methods, e.g., GNSS, but also by using aerial photos and satellite images. All these data are stored in an Oracle database which is the basis of the so-called NascaGIS (see, e.g., [16]). Another important prerequisite for the astronomical approach is a digital elevation model (DEM) because the astronomical altitude or elevation angle depends on the surrounding landscape. Therefore, the results of the Shuttle Radar Topography Mission (SRTM) as well as a DEM generated from ASTER satellite data are used [17]. By definition, the plane of the astronomical horizon is perpendicular to the plumb line at the observer's point. Mountains, valleys or buildings are in the observed direction, so this theoretical astronomical horizon deviates by the elevation angle h, which can be several degrees from the actual horizon (see Figure 9). A star rises at point P\({}_{0}\) with the azimuth \(\alpha_{0}\); however, it only becomes visible at point P\({}_{\rm H}\) with the azimuth \(\alpha_{\rm H}\) (without refraction effects). The same applies to setting stars. Therefore, there has to be a correction of the azimuth, depending on the elevation angle. According to [PERSON] [18] (p. 107), for elevation angles less than 5 degrees, azimuth correction with sufficient accuracy is obtained according to Equation (4), where h is the elevation angle above the astronomical horizon and \(\varphi_{0}\) is the geographical latitude at the observer's point P\({}_{0}\) (see Figure 9). \[\Delta\alpha=\frac{\rm h}{\tan\varphi^{*}}\ \text{with}\ \varphi^{*}=\ 90^{\circ}\ -\ \varphi_{0} \tag{4}\]  
For the Nasca region (\(\varphi_{0}\approx 15^{\circ}\)), the corrections in the azimuth of the stars are shown in Table 1. Corrections in the azimuth for the corresponding elevation angle must therefore be observed. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**h** & **1\({}^{\circ}\)** & **2\({}^{\circ}\)** & **3\({}^{\circ}\)** & **4\({}^{\circ}\)** & **5\({}^{\circ}\)** \\ \hline \(\Delta\alpha\) & \(0^{\circ}16^{\prime}\) & \(0^{\circ}32^{\prime}\) & \(0^{\circ}48^{\prime}\) & \(1^{\circ}04^{\prime}\) & \(1^{\circ}20^{\prime}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Corrections in the azimuth for the corresponding elevation angle. Figure 9: Change in azimuth and elevation angle depending on the terrain [17]. Depending on whether the stars are rising or setting, the azimuth at point P\({}_{\rm H}\) is derived from the following equation:  
\[ \begin{array}{ll}\text{For rising stars:}&\alpha_{\rm H}=\alpha_{0}-\Delta \alpha\\ \text{For setting stars:}&\alpha_{\rm H}=\alpha_{0}+\Delta\alpha\end{array}  \tag{5}\]  
It should be noted that the equations refer to the Southern Hemisphere; the signs would be in the Northern Hemisphere and vice versa. Further azimuth corrections must be considered because of the atmospheric effects of absorption and extinction, since the visibility on the horizon depends on the atmospheric conditions such as pollution, haze and clouds. According to local people, visibility near the horizon has decreased enormously in the past decades. According to investigations by [19] (p. 161), the elevation angle close to the horizon for the first and last visibility of a star is roughly the same as its brightness. The brightness of a star is given by a special system of stellar magnitudes. Faintest stars have the highest value and the brightest stars the lowest. Polaris, the North Pole Star, is of Magnitude 2, while the faintest star visible to the naked eye under very good conditions is of Magnitude 6.