Archaeoastronomical work on the Intihuatana in Machu Picchu
Archaeoastronomical studies at the Intiwatana of Machu Picchu with Professor Benjamin Sánchez Fernández, Doctor mining engineer and professor at the University of Oviedo, Spain
- Anselm Pi Rambla
USE OF DIGITAL MODELS FOR THE ASTRONOMICAL INTERPRETATION OF INTIWATANA OF MACHU PICCHU
In this Works are used oriented digital models to make the astronomical interpetation of the intiwatana of machu pichu, which was carved into a granite rock with the course to know the different seasons of the solar year.
For the digital model of the Intiwatana and its environment it was necessary to carry out a field work that was basically on positions with absolute coordinates using a GPS navigator a lifting speedometer accuracy with electronic total station and reflection and Miniprisms angular sun observations, using the total station to determine the direction of true north.
The field work was done on 20 and 21 of June in 2000, obtaining the refered values of the WGS-84 system.
Latitude: 13 ° 9 '47.3 "S, Longitude: 72 ° 32' 44.5" W; Ellipsoid height: 2500 m.
Because of the mountains surrounding the citadel of Machu Picchu have a quite pronounced relief, in order to know its profile in areas where the sun rises and sets, horizontal and zenith angles of the highlights of the horizon were taken. These measurements are also oriented to true north with the data from the solar observation.
To refer to true north coordinates of the measured points in an arbitrarily oriented system, it was necessary to solve the astronomical triangle formed by the peak position of the station point, the position of the center of the sun and the Earth's north pole. The data needed for this calculation were the geographical coordinates, latitude and longitude, obtained by GPS station point; the exact time it was noted in the sun, expressed in T.U. (Standard time + 5 hours); and the values of the declining, semidiameter apparent when the sun over Greenwich antimeridiano that were obtained from the yearbooks for instant astronomical observation. Once solved the astronomical triangle position 67.991 degrees azimuth to the origin of horizontal angles allowing the guide to true north taquimétrico survey conducted simply by making a turn (in topographical sense) of -67.991 degrees was obtained using as center turning the measurement station.
For astronomical interpretation of Intiwatana among the many possibilities that exist, in this work it was chosen to study the shadows on the monolith at the moment of sunrise over mountains in singular dates, such as solstices June and December, the equinoxes and the passage of the sun through the zenith and antizenith the place of observation.
he results obtained were:
June solstice (June 21)
Azimuth: 68.240 degrees; Zenith angle: 84.600 degrees
December solstice (December 21)
Azimuth: 124.408 degrees; Zenith angle: 89.088 degrees
Equinoxes (March 20 and September 22)
Azimuth: 96.779 degrees; Zenith angle: 86.444 degrees
Cenit (February 14 and October 28)
Azimuth: 112.149 degrees; Zenith angle: 86.763 degrees
Antizenith (April 24 and August 17)
Azimuth: 81.435 degrees; Zenith angle: 86.950 degrees
From a several of photographs taken of the Intiwatana, from different perspectives and using a computer program, a photogrammetric digital model of the monolith mentioned was determined. The program used convergent part of frames of object to be reconstructed digitally, and requires that the frames completely sprinkle on the object, so that in each pair of adjacent frames there are at least three common and easily identifiable points.
The program calculates the model according to the following process:
* Determine the coordinates (x, y, z) of the points of making photographs.
* Calculate the angles of orientation of the frame in space.
* Find the coordinates (x, y, z) of each point on the object identified.
Once we know the coordinates of each point on the object labeled it is possible to build a model using wired lines connecting the dots. This can be defined wireframe surfaces and textures give them obtained by the photographs.
INTERPRETATION OF RESULTS
If the representation is observed in plant obtained topographic digital model, you can see that the upper parallelepiped of Intiwatana is oriented such that the bisectors of the angles formed by the faces coincide quite precisely with the geographic directions north, south, east and west. Western edges of the upper platform Intiwatana, have an alignment parallel to the base of the upper parallelepiped, so that their bisector also indicates the west direction. The western part of the platform seems to be quite adequate for the observations of the shadows cast by the sun at dawn.
At dawn on June solstice, step by antizenith, equinox, passing through the zenith and December solstice shows that the sun's shadow is projected on the upper platform of the Intiwatana, particularly on the edges to the west, proving as shadow moves over them, being the northwest ridge best suited to observe the zenith passage and December solstice. For other dates can be used either edges.
In terms of precision that could determine these dates interest depends on the daily variation in the sun's declination in before and after the same day, is very small at the solstices, but the rest is variation more important, and given the distance from which the shade, which is about 0.6 meters, the daily movement thereof is approximately 5 mm is projected magnitude that is perfectly observable and that could determine without any uncertainty any of these dates, including the zenith passage, that would serve to know precisely the cycle of the solar year (tropical year) and as a consequence have a tool for measuring time.