ASTRONOMICAL ORIENTATION IN OLLANTAYTAMBO, PERU
SEAC 2014, Malta 22-26 Sept.
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.cz
b 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
Abstract
Method
We 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.
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 Fig. 3: Precise large compass,
quantity. Thus, the compass- © D. Lampířová, 2010.
measured directions must be
corrected.
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
Introduction
Service. It is, however, more precise to measure it. It can be done with
In the mountains, we do not see sunrise/sunset at the theoretical, zero sufficient precision for our purpose by handy GPS. From the
horizon, but at an elevation angle, given by the local topography. For a coordinates measured by the GPS of a baseline, we can compute the
topography model we make use of the online digital elevation astronomical azimuth. Then we measure the direction of that baseline
model ASTER GDEM, obtainable on: http://www.gdem.aster.ersdac.or.jp. 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
Fig. 1 shows the astronomical azimuths
of the Sun for the geographic latitude
of Cusco area, for sunrise and sunset at
solstices.
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
Fig. 2: Terrain profiles were based on the success.
ASTER GDEM.
Fig. 4: Terrain profile with
observation point in TS was
computed from north to
south. The red line shows the
sunrise on winter solstice.
Figs. 5a,b: The Temple of the Sun,
© K. Hanzalová, 2012.
Fig. 7: A small temple above
the TS, © K. Hanzalová, 2012
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.
Fig. 6: The red lines show the astronomical azimuths of the rise of
Pleiades from TS, computed for 1000,
1500 and 2000 A.D.
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. 14 right: The terrain
profile was made from
East to West. The red line
shows
the
sunrise
astronomical azimuth at
summer solstice.
Fig. 9: Near and below the TS is a pyramid with “windows“
(see arrows), © Salazar and Salazar 2005.
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. 12: Point P at the corner of the pyramid and a line to and beyond
the Inca face during sunrise at their winter solstice.
Fig. 10: View on the pyramid during sunrise at the winter
solstice. © Salazar and Salazar 2005.
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
Finally we tested a flat pyramid in Ollantaytambo near Urubamba river. west side of the pyramid via its top to the sunrise at the summer solstice above the
The photos here are taken from Salazar and Salazar (2005). We used Urubamba river is 111.7°(see our Fig. 15), derived by means of Google Earth tools.
ASTER GDEM and discovered that sunlight has specific orientation during It was checked by the terrain model, derived for this observational point P, see the
summer and winter solstices (see Figs. 9, 10, 11, and 12).
red line in Fig. 14, showing the azimuth about 112°; the agreement between results in
Figs. 14 and 15 is also excellent.
Conclusion
The authors proceed to test hypothesis about the astronomical-solarsolstice 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.
Recommended literature
Fig. 11: View on pyramid during the sunrise at summer solstice.
© Salazar and Salazar 2005.
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°.
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, 2005
PROTZEN, 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.