ASTRONOMICAL ORIENTATION IN OLLANTAYTAMBO, PERU

HANZALOVÁ K. a, KLOKOČNÍK J. b, J. KOSTELECKÝ c

a CTU in Prague, Faculty of Civil Engineering, Department of Geomatics, Czech Republic, karolina.hanzalova@fsv.cvut.czb Astronomical Institute of the Academy of Sciences of the Czech Republic, Ondřejov Observatory

jklokocn@asu.cas.cz, www.asu.cas.cz/~jklokocn c Research Institute for Geodesy, Topography and Cartography, Zdiby 98, Czech Republic, kost@fsv.cvut.cz

SEAC 2014, Malta 22-26 Sept.

AbstractWe tested possible astronomical orientation of various objects in Ollantaytambo, Inca place in Peru. We made our own measurements (by a precise compass and handy GPS) on the spot, using method completely different from previous researchers and we also employed satellite-derived digital model of terrain (DTM). Astronomical azimuths were derived from the magnetic measurements. Independently, the DTM was used to reconstruct terrain as observed from several points in various parts of Ollantaytambo. The azimuths needed for solstices Sun rises/sets were not found. Finally we tested shadows in solstices at the flat pyramid downstairs in Ollantaytambo at the Urubamba river. The DTM was used to reconstruct terrain at the valley and surrounding mountains to account for azimuth change at the sunrise at the bottom of the pyramid. For the winter solstice, the astronomical azimuth of the sunrise above the local horizon (mountains are behind the valley) should be and actually is 62°, checked by the DTM (62-63°). For the summer solstice sunrise, both ways provide 112°±1°. So, we found and demonstrated the astronomical-solar-solstice orientation of the pyramid. The result is open for interpretation by archeologists and historians.

Introduction

Fig. 1 shows the astronomical azimuths of the Sun for the geographic latitude of Cusco area, for sunrise and sunset at solstices.

In the mountains, we do not see sunrise/sunset at the theoretical, zero horizon, but at an elevation angle, given by the local topography.  For a topography model we make use of the online digital elevation model  ASTER GDEM, obtainable on: http://www.gdem.aster.ersdac.or.jp.

Fig. 2: Terrain profiles were based on the ASTER GDEM.

Method

We measured and computed astronomical azimuths of various alignments in the archaeological locality Ollantaytambo. The alignments were measured by a large and precise compass (Fig. 3), with precision ±1°, for rough (irregular) walls within 1-2°. The azimuths derived from reading the compass are, however, related to the magnetic pole, which does not coincide with the pole of rotation of the Earth, which is an astronomical quantity. Thus, the compass-measured directions must be corrected.

Fig. 3: Precise large compass, © D. Lampířová, 2010.

The difference in the horizontal direction between these two is called magnetic declination. It can be read from a model, provided by NGDC (National Geophysical Data Center) of NOAA Satellite and Information Service. It is, however, more precise to measure it. It can be done with sufficient precision for our purpose by handy GPS. From the coordinates measured by the GPS of a baseline, we can compute the astronomical azimuth. Then we measure the direction of that baseline by a compass and compare both directions. The difference is a good approximation for the correction we need. The final accuracy of the astronomical azimuth derived by this way is not worse than ±2°.

Results

We tested orientation of the main wall of the Temple of the Sun (TS, Figs. 4a,b), Temple of water (TW, Inca fountain), a stone nearby, etc. Nowhere we confirmed astronomical, solar, solstice orientation. The astronomical azimuth of the wall of the TS is 53°. We used the model from ASTER and created terrain profiles (Fig.2) . The astronomical azimuths of sunrise on June solstice were then calculated, namely 58 - 59° for TS and 32 - 31° for TW, north of east (Fig. 4). We tested also the rise of the Pleiades, which have a similar declination as the Sun in June at the winter solstice. We computed their rises for the the epochs 2000, 1500 and 1000 A.D (Fig. 6). We tested a small temple on the top of Ollantaytambo (Fig. 7) above the TS, but again without any success.

Figs. 5a,b: The Temple of the Sun, © K. Hanzalová, 2012.

Fig. 4: Terrain profile with observation point in TS was computed from north to south. The red line shows the sunrise on winter solstice.

Fig. 7: A small temple above the TS, © K. Hanzalová, 2012

Fig. 6: The red lines show the astro-nomical azimuths of the rise of Pleiades from TS, computed for 1000, 1500 and 2000 A.D.

Fig. 8 right: View on the TS at the winter solstice (left), the Sun, observed from TS, rises behind the Inca face (right). © Salazar and Salazar 2005.

ASTER GDEM: obtainable on: http://www.gdem.aster.ersdac.or.jp. EDGAR E.: Cusco and the Sacred Valley of the Incas, Tankar E.I.R.L., Lima, 2005PROTZEN, J. P.: Inca architecture and construction at Ollantaytambo, Oxford University Press, 1993. SALAZAR ELORRIETA FERNANDO E., SALAZAR ELORRIETA. ZAWASKI, M. J., MALVILLE KIM, J.: An archaeoastronomical survey of major Inca sites in Peru, Archaeoastronomy, 29 (2007), 20-38.

Recommended literature

The authors proceed to test hypothesis about the astronomical-solar-solstice orientation of artifacts in Ollantaytambo. There is a possibility of the winter solstice connection between the pyramid at the Urubamba river, the Temple of the Sun and the Inca face and of the summer solstice connection of the pyramid and Urubamba river valley. Based on spherical trigonometry, recent digital terrain model and geodetic measurements and computations, we are able to explain what was shown by photos in Salazar and Salazar (2005). It means that we are able to demonstrate a possibility of the solar-solstice orientation in Ollantaytambo. Whether this connection has any cultural significance or not cannot be decided by the authors of this paper (geodesists + astronomer) but by other specialists. But it is logical that there might be a cultural significance of the discussed alignments for example for agricultural (practical) purposes and for related ceremonials/rituals.

Conclusion

Fig. 15. Astronomical-solar-summer solstice direction connecting the pyramid from point P2, its western slope and its top with the direction to Urubamba river valley.

Fig. 14 right: The terrain profile was made from East to West. The red line shows the sunrise astronomical azimuth at summer solstice.

Fig. 13: The terrain profile with observation point on the pyramid (P). The red line shows the sunrise at winter solstice. The astronomical azimuth was calculated to be 62 – 63°.

We also considered the western slope of the pyramid and time of sunrise at their summer solstice (Fig. 11). The astronomical azimuth of the slant line going from west side of the pyramid via its top to the sunrise at the summer solstice above the Urubamba river is 111.7°(see our Fig. 15), derived by means of Google Earth tools. It was checked by the terrain model, derived for this observational point P, see the red line in Fig. 14, showing the azimuth about 112°; the agreement between results in Figs. 14 and 15 is also excellent.

Fig. 12: Point P at the corner of the pyramid and a line to and beyond the Inca face during sunrise at their winter solstice.

We considered a point P (Fig. 12) at the corner (east rectangle) of the pyramid down by the riverside. There is a line connecting the east rectangular “platform” at the Urubamba river, going along the Inca road up to vicinity of the Temple of the Sun and then over the valley north of terraces and storehouses and the bearded man face in the direction to the Inca face - see the plans presented as Figs. 1.2 and 1.19 in Protzen (1993) or in Salazar and Salazar (2005). The astronomical azimuth of this slant line is 61.7° (see our Fig. 12), derived by means of Google Earth tools. It is checked by the terrain model for this place, see the red line in Fig. 13, showing the azimuth about 62-63°. Accounting for possible inaccuracy of both approaches, the agreement between results in Figs. 12 and 13 is excellent. Salazar and Salazar (2005) noted that the ray of sunlight falls in winter solstice to a corner of the pyramid and that chronicler Guamana Poma (1613) wrote that by means of sunshine falling on some windows the dates of sowing and harvest were estimated. Was there any temple? Satellite photos on Google Earth support this opinion.

Fig. 11: View on pyramid during the sunrise at summer solstice. © Salazar and Salazar 2005.

Finally we tested a flat pyramid in Ollantaytambo near Urubamba river. The photos here are taken from Salazar and Salazar (2005). We used ASTER GDEM and discovered that sunlight has specific orientation during summer and winter solstices (see Figs. 9, 10, 11, and 12).

Fig. 10: View on the pyramid during sunrise at the winter solstice. © Salazar and Salazar 2005.

Fig. 9: Near and below the TS is a pyramid with “windows“ (see arrows), © Salazar and Salazar 2005.